Pith. sign in

Paper Citation Record · LEDGER

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function

As of 18 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2504.12604.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2504.12604 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:40:13.517328Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

47 of 47 outbound references displayed

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  • verified fuzzy46
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5cc60925-5ee9-4e63-93e2-43cd1986ba2e · outbound

This paper cites Isodual codes over Z2k and isodual lattices,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Isodual codes over Z2k and isodual lattices,

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.193920Z digest=sha256:0ebce2758455efdb49a69638beae74773e56f275948fd0896b4439372cb07383

Observation 03cd96df-3b9d-4420-b66d-cf1937af6201 · outbound

This paper cites Type II co des, even unimodular lattices, and invariant rings,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Type II co des, even unimodular lattices, and invariant rings,

Reference 2

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raw_fallback, observed 2026-08-16T12:40:14.629511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.201094Z digest=sha256:a081fbc066e5801c5df2e2133d7d3347e4f60b0a58e4e99f7f87bba9ccf632d6

Observation a70d1889-aa26-4063-9726-0743903760fd · outbound

This paper cites On the complete weight enumerator o f Reed-Solomon codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function On the complete weight enumerator o f Reed-Solomon codes,

Reference 3

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.207031Z digest=sha256:cb66a9eb6c6ac71b180c2765c8ded31c6b0e374a86bee2b74ad252fdd820d01f

Observation 6f56f16b-5d1b-4a8d-b26f-f629e2a73c72 · outbound

This paper cites Secrecy gain of formally unimodular lattices fro m codes over the integers modulo 4,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Secrecy gain of formally unimodular lattices fro m codes over the integers modulo 4,

Reference 4

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.216427Z digest=sha256:54723f0f331b69f3e94678c8fc88395cdbe39fb6161456eb42c71f58717ae36f

Observation 1b7fb62e-4921-4a63-ad83-f1751761a26e · outbound

This paper cites Quaternary qu adratic residue codes and unimodular lattices,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Quaternary qu adratic residue codes and unimodular lattices,

Reference 5

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.223560Z digest=sha256:6821e476dcaba9ec36c94dd395c1a8813b84a05bf990eb77e996cacf6661b640

Observation 53cd9769-6222-4f02-b036-aeff4b461cda · outbound

This paper cites Type II c odes over Z4,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Type II c odes over Z4,

Reference 6

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.234734Z digest=sha256:b8ac50d19a3c5bf8179fe1bb12905145cd7a50879cfe62d89fff1f8427d49e23

Observation 36413470-5d01-4c34-8d82-bb59b34289de · outbound

This paper cites MacWilliams identities and matroid polynomi als,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams identities and matroid polynomi als,

Reference 7

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.242408Z digest=sha256:771dc7858813eb6876cc8e61ba6dff8cbe2aaadf33606e50e15537beed71ef3e

Observation 92c42aff-47ce-417f-93a4-da3d7dceeb4b · outbound

This paper cites Jacobi forms over totally real fields and codes over Fp,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Jacobi forms over totally real fields and codes over Fp,

Reference 8

Resolution
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raw_fallback, observed 2026-08-16T12:40:14.510015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.248236Z digest=sha256:c2218e958a91435583476bd48efba4b12384ab6086c022507f194178417d21ed

Observation 6418b40d-1fcb-477f-a865-12ea9c1b2513 · outbound

This paper cites Sphere packings, lattices and gro ups,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Sphere packings, lattices and gro ups,

Reference 9

Resolution
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raw_fallback, observed 2026-08-16T12:40:14.489282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.255904Z digest=sha256:f2830c84793ff4df7263633b942149df8d0cf392ef83f121288ea8b8f7cf70ed

Observation 1166d345-95d2-46ad-a008-ab29875041b9 · outbound

This paper cites Self-dual codes over the integers modulo 4,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Self-dual codes over the integers modulo 4,

Reference 10

Resolution
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raw_fallback, observed 2026-08-16T12:40:14.467678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.261852Z digest=sha256:690b1b973dc63c9421300fc4e980406c6e4c11434fd79f68a8b9d571eb37a716

Observation 878f3c95-fbee-48fe-992a-64876136ac3f · outbound

This paper cites Type II self -dual codes over finite rings and even unimodular lattices,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Type II self -dual codes over finite rings and even unimodular lattices,

Reference 11

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.267347Z digest=sha256:287734cf7e4ddd5554f316239137fab5216416358c51c2127b9749b3cd5b6e82

Observation 38439e7d-7472-46c6-84c2-f04dac8ca930 · outbound

This paper cites Lattices and codes: A course partially bas ed on lectures by Friedrich Hirzebruch,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Lattices and codes: A course partially bas ed on lectures by Friedrich Hirzebruch,

Reference 12

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raw_fallback, observed 2026-08-16T12:40:14.428416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.273383Z digest=sha256:839b50f32b9c7bf0673dc84b564fac898ab87ddb26a7e97932010b1a355f1178

Observation dc327ea8-730a-4547-91b6-740475ea1464 · outbound

This paper cites On the residue codes of extremal type II Z4-codes of lengths 32 and 40,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function On the residue codes of extremal type II Z4-codes of lengths 32 and 40,

Reference 13

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.280233Z digest=sha256:4f0398a12b48b0d346250fc7d8076bc3d71d8ab7d19b8e0b4cfd0522df9c99f3

Observation cb3ff06d-407b-4bc4-872f-dfb9ba7ed5c2 · outbound

This paper cites Optimal self-dual Z4-codes and a unimodular lattice in dimension 41,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Optimal self-dual Z4-codes and a unimodular lattice in dimension 41,

Reference 14

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.287050Z digest=sha256:3f6c0f809e2941e95403e34c64c8350768477e1004cb5d7eba0706a87bf3c1b3

Observation 1ba704c6-1246-48b1-93a3-880cdda31320 · outbound

This paper cites On the existence of extremal typ e II Z2k-codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function On the existence of extremal typ e II Z2k-codes,

Reference 15

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.297324Z digest=sha256:7e62a9cec8f9aa9bf66c7eb2ae896b831ebe98587fa0c413ec913f6e376aaa06

Observation ea0d6c10-7039-4397-8fac-cac886fa5169 · outbound

This paper cites Hilbert modular surfaces,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Hilbert modular surfaces,

Reference 16

Resolution
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.305675Z digest=sha256:c32c603964eb6f5457de2fd2314202812cf39344fa073af37def0c1dfc8bbf05

Observation d481e53e-c15f-4646-9159-c28e4b785b9e · outbound

This paper cites The ring of Hilbert modular forms for re al quadratic fields of small discriminant,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function The ring of Hilbert modular forms for re al quadratic fields of small discriminant,

Reference 17

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.313721Z digest=sha256:417c2af4bf5191a1677f0af78e9a4a0f1c14039d4351e4de306a8184a4d50f66

Observation b9271ad9-6747-4534-bc48-5b4abb0c5d90 · outbound

This paper cites Gesammelte Abhandlungen,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Gesammelte Abhandlungen,

Reference 18

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.319849Z digest=sha256:d98a1bb69c43d23989eaca90a6eb98886efcd375988f013efc858996aa668b0a

Observation 73b0c614-0287-4435-9dc3-a6d273c5af16 · outbound

This paper cites Complete weight distr ibutions and MacWilliams identities for asymmetric quantu m codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete weight distr ibutions and MacWilliams identities for asymmetric quantu m codes,

Reference 19

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.332986Z digest=sha256:957e4d51cc380bf10394132cec548a9ccfe28b57b6faa9295905bdfca7d0ca20

Observation 5b8fb3e9-60bb-4aae-8436-15fd3f9fe620 · outbound

This paper cites Self-dual codes, lattices, and in variant theory,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Self-dual codes, lattices, and in variant theory,

Reference 20

Resolution
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raw_fallback, observed 2026-08-16T12:40:14.271287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.340234Z digest=sha256:38635c03f380870fafa66bfa9177cd7850e0f3eca5ffd32fa09a19abed7ec336

Observation 57c5fc9f-428e-427d-8321-f676365ea09f · outbound

This paper cites MacWilliams identities for m-tuple weight enumerators,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams identities for m-tuple weight enumerators,

Reference 21

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.346211Z digest=sha256:cf37b76e8c79687b0e4083f1e8c896ca05e5ac5f5b3831dec07bc8ca897a27c6

Observation ba985867-7eac-45b1-9e4f-0ec25c7967e3 · outbound

This paper cites Uber die identitat von MacWilliams fur die ge wichtsfunktion von codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Uber die identitat von MacWilliams fur die ge wichtsfunktion von codes,

Reference 22

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raw_fallback, observed 2026-08-16T12:40:14.233109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.353513Z digest=sha256:31a9fd9c0528f155cf9d88c7b4769737d4ee114a4ea77523c98b48701edf297a

Observation 8db56091-986e-4c8a-81b1-ec181ce40ed7 · outbound

This paper cites Complete weight enumerators of generalized Kerdock code and related linear codes over Galo is ring,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete weight enumerators of generalized Kerdock code and related linear codes over Galo is ring,

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:14.213680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.359747Z digest=sha256:3f257b49352fdcdce0e2de456713e3fefca77a8e33f5240f4c2d21394a248c8d

Observation a8599e86-a06f-4e95-97b6-d050a79bb94c · outbound

This paper cites A complete MacWilliams t heorem for convolutional codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A complete MacWilliams t heorem for convolutional codes,

Reference 24

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raw_fallback, observed 2026-08-16T12:40:14.190836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.367472Z digest=sha256:4dd3952e6e18a01a8dcf1b67b98b0c4ed2246fa628106c9f7396ab5e9f264237

Observation 5908aa28-be99-4893-8fdc-971a6779506d · outbound

This paper cites Complete weight en umerators of some linear codes and their applications,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete weight en umerators of some linear codes and their applications,

Reference 25

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raw_fallback, observed 2026-08-16T12:40:14.167828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.373686Z digest=sha256:b27f1defe56e4f70272fe93649aece218a9a211bc2f3831c0d5fec43e9573170

Observation da3fd0cb-0cc7-43d5-bfed-76f91690767d · outbound

This paper cites Complete weight enumerators of som e cyclic codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete weight enumerators of som e cyclic codes,

Reference 26

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raw_fallback, observed 2026-08-16T12:40:14.150589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.379246Z digest=sha256:de6744794252b6793c25da7daca0405894b60032333f4091b465c99df9e5dfdc

Observation 60fb63c5-e6d1-4155-aef8-31d1da83f3c0 · outbound

This paper cites A theorem on the distribution of wei ghts in a systematic code,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A theorem on the distribution of wei ghts in a systematic code,

Reference 27

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raw_fallback, observed 2026-08-16T12:40:14.132744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.385057Z digest=sha256:1b6df350919a2cfa4c3ec3e287e05967f8441a3173c33a2ba8e40e661a5bcd1a

Observation d26450b9-cb6f-4f0c-9b63-a179ff68dde5 · outbound

This paper cites The MacWi lliams identities for nonlinear codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function The MacWi lliams identities for nonlinear codes,

Reference 28

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raw_fallback, observed 2026-08-16T12:40:14.108780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.392198Z digest=sha256:f8693f6b51119889acd33a83ed1904c2abf71baf5ae3913ca95e3e1e5bfeaec8

Observation 99743c09-c620-45c2-b18e-4d5a18b06a85 · outbound

This paper cites Complete w eight enumerators of generalized doubly-even self-dual co des,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete w eight enumerators of generalized doubly-even self-dual co des,

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:14.087736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.399529Z digest=sha256:f7d924a41f432b143918a35045667f3ec1eb3de6bdf050652f7880e36293bd9b

Observation 503c5bfd-7eb0-45c6-be2b-5c1b8b62e8a1 · outbound

This paper cites A course in arithmetic,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A course in arithmetic,

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:14.066930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.405314Z digest=sha256:9b128fd2339bff0e4b6fd9c68ea3f9e7536bdfa8596c2564d753e53fbd66aa12

Observation d938bbf6-7d61-4376-ad83-faa4cd1768a8 · outbound

This paper cites Construction of self-dual cod es over Z2m,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Construction of self-dual cod es over Z2m,

Reference 31

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raw_fallback, observed 2026-08-16T12:40:14.047479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.411123Z digest=sha256:2be06cb93196f3d92e3fb8540d87da580331b7c720f6a99fbf71d3bec6eb4407

Observation ea5f30e2-d820-4f70-af16-bf06ac443318 · outbound

This paper cites Codes and modular forms: a dictionary,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Codes and modular forms: a dictionary,

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:14.029208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.420023Z digest=sha256:522572268d309de7e49481660508b6bb9f6891e666e83d9a52395038844cfc37

Observation 9edf9022-66dd-48ce-a42e-4e18cb2728cb · outbound

This paper cites A note on a basic exact se quence for the Lee and Euclidean weights of linear codes over Zl,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A note on a basic exact se quence for the Lee and Euclidean weights of linear codes over Zl,

Reference 33

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raw_fallback, observed 2026-08-16T12:40:14.009731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.428085Z digest=sha256:85779c5691f6de48893951e0ee1ba39ee18efe3cdb4d2d94f2abaa80b3412457

Observation 019e9159-cbe5-4556-bde2-72be142cf1a0 · outbound

This paper cites Expanding self-ortho gonal codes over a ring Z4 to self-dual codes and unimodular lattices,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Expanding self-ortho gonal codes over a ring Z4 to self-dual codes and unimodular lattices,

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.989585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.434998Z digest=sha256:af97bcc0df889f3630e3c022bdf211ae6ae6dc979398a11068592f46817fcd6f

Observation aea95a0c-6262-4df7-bfa6-d43f1373c86d · outbound

This paper cites A new MacWilliams type identity for line ar codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A new MacWilliams type identity for line ar codes,

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.970521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.441443Z digest=sha256:34b5fe919d40d1c5f98b48470e714a0a8f98cfd6e6c998c69df3972413a0caa3

Observation b0cd7e7c-7aa6-4a10-8392-2eaf23446d46 · outbound

This paper cites The complete weight enumerator for codes over Mn× s(R),.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function The complete weight enumerator for codes over Mn× s(R),

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.950327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.448085Z digest=sha256:584dbf7500ddf38ba067dcffbaa74fa741c47d9c477e51ac24d212f22c3a0873

Observation 95c01905-79e7-45e5-8d77-9185c8cfe86c · outbound

This paper cites MacWilliams identity for m-spotty Lee weight enumerators,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams identity for m-spotty Lee weight enumerators,

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.930600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.453126Z digest=sha256:97513ea510e9125e474c061cce3888a014485f254786f40e55919165d9d96fea

Observation 1cb2e7b3-1e23-47e3-b5b3-5fe24207cad0 · outbound

This paper cites Complete m-spotty weight enumerators of binary codes, Jacobi forms, a nd partial Epstein zeta functions,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete m-spotty weight enumerators of binary codes, Jacobi forms, a nd partial Epstein zeta functions,

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.898151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.458855Z digest=sha256:37131d0929a819027394dc4999e883c1249a780a02cdbe77d7bae7c24e065fdf

Observation c891caf2-e2b7-49d3-8b00-1029e6f92b68 · outbound

This paper cites The MacWilliams identity for linear codes over Galois rings,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function The MacWilliams identity for linear codes over Galois rings,

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.877676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.465534Z digest=sha256:33c38ab5c742de491bd900fded7e140c58b773f3ec924bc8c622b241611ccb50

Observation 9afa7f79-b486-42e2-8e3d-c7b1009f8b87 · outbound

This paper cites Complete weight enumera tors of two classes of linear codes,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete weight enumera tors of two classes of linear codes,

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.855101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.470913Z digest=sha256:203891e617f28f1ea3c3746ea813f04110ed8b0f6d79b93649c8d494a2fa33f3

Observation d6ef4589-0244-4a0d-ad2c-793389167e1e · outbound

This paper cites Duality for modules over finite rings and app lications to coding theory,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Duality for modules over finite rings and app lications to coding theory,

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.831663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.476821Z digest=sha256:acabf6a2c4fdeac9e08bb0b0f0a9f3dd83ee842152e3ffe4e5b027bbc40bdc44

Observation d681e9cf-2e5e-4998-9106-bfa5553e3d23 · outbound

This paper cites Foundations of linear codes defined over fini te modules: the extension theorem and the MacWilliams ident ities,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Foundations of linear codes defined over fini te modules: the extension theorem and the MacWilliams ident ities,

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.811182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.483464Z digest=sha256:d0f678afb1fb24672f8e92917a550b6f9b821df008cceb17bff11a0515fb0057

Observation 44a0ed9e-0459-408b-9d6a-a1bc93d7c2f1 · outbound

This paper cites Applications of finite Frobenius rings to th e foundations of algebraic coding theory,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Applications of finite Frobenius rings to th e foundations of algebraic coding theory,

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.791853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.488785Z digest=sha256:6062420eb739f8382dc26ad1ff451360cefcb6cb54cabcd4b505270a7d8ac44d

Observation f743f51c-4d1d-495a-aa71-2b9c9a93e5a6 · outbound

This paper cites A construction of linear code s and their complete weight enumerators,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A construction of linear code s and their complete weight enumerators,

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.773127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.495122Z digest=sha256:b22369e7922cfad84a8a867a931be8486d54b04976191684cfc167fc1c4c2df0

Observation 9ecfd7ba-fbfd-42c5-9147-4fe775f55acc · outbound

This paper cites Constructions of formally self- Dual codes over Z4 and their weight enumerators,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Constructions of formally self- Dual codes over Z4 and their weight enumerators,

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.748115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.502082Z digest=sha256:56d0b2adee3b47a5fcd3df06fdd0d1f578f8e6e30c2ea02ad667607f31f280bd

Observation 3e344a40-859d-4df5-92d0-6dc5345457fb · outbound

This paper cites On the MacWilliams theorem ov er codes and lattices,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function On the MacWilliams theorem ov er codes and lattices,

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-16T12:40:13.510514Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T12:40:13.510514Z digest=sha256:7edff4afcf1eb6a935dfe62eb4ffa4a50975e78002df4aafe110fd3ca9568bd9

Observation 58039656-7e96-4fd7-a6bf-18dd578d4ec4 · outbound

This paper cites MacWilliams theory over Zk an d nu-function over lattices,.

Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams theory over Zk an d nu-function over lattices,

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T12:40:13.727110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-16T12:40:13.517328Z digest=sha256:9bc9c3d13e19afe851df9f30cca693ac134b4191e8691874add17cde8a3c9663

Pith citing papers

No inbound Pith citation observations are available.