Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T12:40:13.517328Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T12:40:13.517328Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
47 of 47 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 5cc60925-5ee9-4e63-93e2-43cd1986ba2e · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Isodual codes over Z2k and isodual lattices,
Reference 1
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.
Observation 03cd96df-3b9d-4420-b66d-cf1937af6201 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Type II co des, even unimodular lattices, and invariant rings,
Reference 2
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.
Observation a70d1889-aa26-4063-9726-0743903760fd · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function On the complete weight enumerator o f Reed-Solomon codes,
Reference 3
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.
Observation 6f56f16b-5d1b-4a8d-b26f-f629e2a73c72 · outbound
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
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.
Observation 1b7fb62e-4921-4a63-ad83-f1751761a26e · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Quaternary qu adratic residue codes and unimodular lattices,
Reference 5
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.
Observation 53cd9769-6222-4f02-b036-aeff4b461cda · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Type II c odes over Z4,
Reference 6
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.
Observation 36413470-5d01-4c34-8d82-bb59b34289de · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams identities and matroid polynomi als,
Reference 7
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.
Observation 92c42aff-47ce-417f-93a4-da3d7dceeb4b · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Jacobi forms over totally real fields and codes over Fp,
Reference 8
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.
Observation 6418b40d-1fcb-477f-a865-12ea9c1b2513 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Sphere packings, lattices and gro ups,
Reference 9
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.
Observation 1166d345-95d2-46ad-a008-ab29875041b9 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Self-dual codes over the integers modulo 4,
Reference 10
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.
Observation 878f3c95-fbee-48fe-992a-64876136ac3f · outbound
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
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.
Observation 38439e7d-7472-46c6-84c2-f04dac8ca930 · outbound
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
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.
Observation dc327ea8-730a-4547-91b6-740475ea1464 · outbound
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
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.
Observation cb3ff06d-407b-4bc4-872f-dfb9ba7ed5c2 · outbound
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
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.
Observation 1ba704c6-1246-48b1-93a3-880cdda31320 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function On the existence of extremal typ e II Z2k-codes,
Reference 15
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.
Observation ea0d6c10-7039-4397-8fac-cac886fa5169 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Hilbert modular surfaces,
Reference 16
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.
Observation d481e53e-c15f-4646-9159-c28e4b785b9e · outbound
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
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.
Observation b9271ad9-6747-4534-bc48-5b4abb0c5d90 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Gesammelte Abhandlungen,
Reference 18
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.
Observation 73b0c614-0287-4435-9dc3-a6d273c5af16 · outbound
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
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.
Observation 5b8fb3e9-60bb-4aae-8436-15fd3f9fe620 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Self-dual codes, lattices, and in variant theory,
Reference 20
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.
Observation 57c5fc9f-428e-427d-8321-f676365ea09f · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams identities for m-tuple weight enumerators,
Reference 21
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.
Observation ba985867-7eac-45b1-9e4f-0ec25c7967e3 · outbound
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
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.
Observation 8db56091-986e-4c8a-81b1-ec181ce40ed7 · outbound
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
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.
Observation a8599e86-a06f-4e95-97b6-d050a79bb94c · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A complete MacWilliams t heorem for convolutional codes,
Reference 24
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.
Observation 5908aa28-be99-4893-8fdc-971a6779506d · outbound
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
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.
Observation da3fd0cb-0cc7-43d5-bfed-76f91690767d · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete weight enumerators of som e cyclic codes,
Reference 26
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.
Observation 60fb63c5-e6d1-4155-aef8-31d1da83f3c0 · outbound
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
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.
Observation d26450b9-cb6f-4f0c-9b63-a179ff68dde5 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function The MacWi lliams identities for nonlinear codes,
Reference 28
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.
Observation 99743c09-c620-45c2-b18e-4d5a18b06a85 · outbound
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
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.
Observation 503c5bfd-7eb0-45c6-be2b-5c1b8b62e8a1 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A course in arithmetic,
Reference 30
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.
Observation d938bbf6-7d61-4376-ad83-faa4cd1768a8 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Construction of self-dual cod es over Z2m,
Reference 31
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.
Observation ea5f30e2-d820-4f70-af16-bf06ac443318 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Codes and modular forms: a dictionary,
Reference 32
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.
Observation 9edf9022-66dd-48ce-a42e-4e18cb2728cb · outbound
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
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.
Observation 019e9159-cbe5-4556-bde2-72be142cf1a0 · outbound
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
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.
Observation aea95a0c-6262-4df7-bfa6-d43f1373c86d · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function A new MacWilliams type identity for line ar codes,
Reference 35
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.
Observation b0cd7e7c-7aa6-4a10-8392-2eaf23446d46 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function The complete weight enumerator for codes over Mn× s(R),
Reference 36
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.
Observation 95c01905-79e7-45e5-8d77-9185c8cfe86c · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams identity for m-spotty Lee weight enumerators,
Reference 37
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.
Observation 1cb2e7b3-1e23-47e3-b5b3-5fe24207cad0 · outbound
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
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.
Observation c891caf2-e2b7-49d3-8b00-1029e6f92b68 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function The MacWilliams identity for linear codes over Galois rings,
Reference 39
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.
Observation 9afa7f79-b486-42e2-8e3d-c7b1009f8b87 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function Complete weight enumera tors of two classes of linear codes,
Reference 40
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.
Observation d6ef4589-0244-4a0d-ad2c-793389167e1e · outbound
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
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.
Observation d681e9cf-2e5e-4998-9106-bfa5553e3d23 · outbound
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
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.
Observation 44a0ed9e-0459-408b-9d6a-a1bc93d7c2f1 · outbound
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
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.
Observation f743f51c-4d1d-495a-aa71-2b9c9a93e5a6 · outbound
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
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.
Observation 9ecfd7ba-fbfd-42c5-9147-4fe775f55acc · outbound
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
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.
Observation 3e344a40-859d-4df5-92d0-6dc5345457fb · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function On the MacWilliams theorem ov er codes and lattices,
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 58039656-7e96-4fd7-a6bf-18dd578d4ec4 · outbound
Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function MacWilliams theory over Zk an d nu-function over lattices,
Reference 47
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.
No inbound Pith citation observations are available.