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Paper Citation Record · LEDGER

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel

As of 19 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2507.10068.

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

pith.paper-citation-record.v1
2507.10068 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:50:44.752156Z

measured 30 of 30 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

30 of 30 outbound references displayed

  • verified exact2
  • verified fuzzy27
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fafc8cc7-51b7-45ba-9e54-ec92369f2157 · outbound

This paper cites Application of Boolean algebra to switching circuit design and to error detection,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Application of Boolean algebra to switching circuit design and to error detection,

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.997600Z

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=2026-08-06T17:50:44.674380Z digest=sha256:1c6c703f0de814e7c2eae21a11c8e4352a4c978f1a37f4b9d0d7e0b25409b208

Observation 75e5671b-3323-4997-99a1-46dad2ba7b49 · outbound

This paper cites A class of multiple-error-correcting codes and the decoding scheme,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel A class of multiple-error-correcting codes and the decoding scheme,

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.990436Z

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=2026-08-06T17:50:44.677897Z digest=sha256:ba3b0460e7a83a6c9b249017412936d9a64762ac77c9a991e4d617b8179c1e58

Observation 000360e5-5f7b-44b6-ac0c-af9940b705db · outbound

This paper cites Reed–Muller codes: Theory and algorithms,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Reed–Muller codes: Theory and algorithms,

Reference 3

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raw_fallback, observed 2026-08-06T17:50:44.983694Z

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=2026-08-06T17:50:44.681396Z digest=sha256:bce749c8f3d523e7fb2bf39a50472b7404c84327f713d5822fa1de8cb6cb370e

Observation a93e296f-e25f-48f0-bf66-d56f233f068e · outbound

This paper cites Channel polarization: A method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Channel polarization: A method for constructing capacity- achieving codes for symmetric binary-input memoryless channels,

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.977455Z

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=2026-08-06T17:50:44.683691Z digest=sha256:dc751c602fb918bb39c0b3c790c947b49579b19bdfb4febeb2416d21ff14d4a6

Observation 0f069c23-f8dc-43f7-9c04-0c385420eda4 · outbound

This paper cites A proof that Reed-Muller codes achieve Shannon capacity on symmetric channels,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel A proof that Reed-Muller codes achieve Shannon capacity on symmetric channels,

Reference 5

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verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.970510Z

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=2026-08-06T17:50:44.686550Z digest=sha256:84e1a118ee538cd11bec4de56ae37a5f3406ae9b6c31518cbb3f6c19754d90fd

Observation 83e32812-7216-4948-8c61-537f50f4eb5c · outbound

This paper cites Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for all Rates Below Capacity,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Reed–Muller Codes on BMS Channels Achieve Vanishing Bit-Error Probability for all Rates Below Capacity,

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.962269Z

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=2026-08-06T17:50:44.690274Z digest=sha256:1524fb8342491fa2608f2c4313611737168c60a55173b63061a017b9a664a38a

Observation 710d7e0f-3878-4f78-ace0-934985c93361 · outbound

This paper cites From Polar to Reed- Muller Codes: A Technique to Improve the Finite-Length Performance,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel From Polar to Reed- Muller Codes: A Technique to Improve the Finite-Length Performance,

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.955851Z

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=2026-08-06T17:50:44.692945Z digest=sha256:297eeb5d7a0b8b8da5dd92ac10a2dc689a186b9f03c4728150270122900012dc

Observation d49921a8-a3e8-416c-8783-887a213848aa · outbound

This paper cites Polar codes: Characterization of exponent, bounds, and constructions,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Polar codes: Characterization of exponent, bounds, and constructions,

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.949677Z

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=2026-08-06T17:50:44.695900Z digest=sha256:155743b35356cf76ceba8b01ee644f78b7065a2929ddcec0fe8c8e53ae498cb8

Observation 7df60277-2c2c-4687-a62a-581b44e587ce · outbound

This paper cites Berman codes: A generalization of Reed–Muller codes that achieve BEC capacity,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Berman codes: A generalization of Reed–Muller codes that achieve BEC capacity,

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.942327Z

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=2026-08-06T17:50:44.698326Z digest=sha256:2170d7c1fbcd28336d906f6d5d5b72aea661baddccd890153fbf6122ee5f9845

Observation bd12d7e3-f998-4754-b999-7b5d961fd459 · outbound

This paper cites Semisimple cyclic and Abelian codes. II,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Semisimple cyclic and Abelian codes. II,

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.933947Z

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=2026-08-06T17:50:44.700520Z digest=sha256:59d13ecb835af980ae0d20658bbff4dc787f691f3626672899d8c16a737ef764

Observation f2e8cce4-845e-47b7-8758-62a0a926a713 · outbound

This paper cites On a family of abelian codes and their state complexities,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel On a family of abelian codes and their state complexities,

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.926291Z

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=2026-08-06T17:50:44.702692Z digest=sha256:528e2a9311f6bfd7c0c09fd0f5a8f427eae6433a922abb0c51ba0a1589284b48

Observation 0ee27266-678d-4a28-bf9d-6f6dc2ebcbcb · outbound

This paper cites Successive Cancellation Ordered Search Decoding of Modified GN-Coset Codes,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Successive Cancellation Ordered Search Decoding of Modified GN-Coset Codes,

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.916068Z

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=2026-08-06T17:50:44.705409Z digest=sha256:5077846e33c5eab163de8510028744dee5ce746da2de88365e112e13630085b5

Observation de562067-97af-4622-a71b-51ac91014525 · outbound

This paper cites A RM-Polar Codes.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel A RM-Polar Codes

Reference 13

Resolution
verified exact
local_arxiv, observed 2026-08-06T17:50:44.794989Z

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=2026-08-06T17:50:44.708435Z digest=sha256:6d6643ed6ec795ba63f7e40e14e77bed5e334657192342c271b461c5c322b573

Observation 15aa886c-7386-4176-aae8-32fd153d084d · outbound

This paper cites Transform domain characterization of abelian codes,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Transform domain characterization of abelian codes,

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.908843Z

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=2026-08-06T17:50:44.711033Z digest=sha256:145e4efeb4eed3ef68737f27d98678039b17f52befd8d07548891c60c80feb50

Observation f5fd2b33-fad2-4b6a-88bd-4c51d16ddeb5 · outbound

This paper cites Reed–Muller codes achieve capacity on erasure channels,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Reed–Muller codes achieve capacity on erasure channels,

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.901769Z

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=2026-08-06T17:50:44.713331Z digest=sha256:94379b806b750fe2290bc10b1d594cfac7e20f09da9cdcc7111b51ee32356b47

Observation c178dcf0-1ec9-4bee-a2b2-16dde96fd7af · outbound

This paper cites Polar codes for channel and source coding,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Polar codes for channel and source coding,

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.895615Z

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=2026-08-06T17:50:44.715622Z digest=sha256:26882f7ad048d85354bb697284448fe472236fd226d905233ed357abe4b0965b

Observation 25f82278-027e-4216-acfd-b36e44e06566 · outbound

This paper cites Complexity-adaptive maximum-likelihood decoding algorithms with a successive cancellation schedule,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Complexity-adaptive maximum-likelihood decoding algorithms with a successive cancellation schedule,

Reference 17

Resolution
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raw_fallback, observed 2026-08-06T17:50:44.888543Z

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=2026-08-06T17:50:44.717841Z digest=sha256:cbf08b95ad2e78a67d058be9c2ce5234cc255d5f001de97412a00a46b4dcafea

Observation e3a3b08c-c45f-4471-b339-b04fe9067c66 · outbound

This paper cites List decoding of polar codes,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel List decoding of polar codes,

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.882422Z

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=2026-08-06T17:50:44.720093Z digest=sha256:771cefbdce136bd5cf656fe99686f729ae074cbe710cf0e37df16ed7e8318112

Observation dc6be65c-dd13-4d17-a990-0b963c5d2a18 · outbound

This paper cites From sequential decoding to channel polarization and back again.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel From sequential decoding to channel polarization and back again

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-06T17:50:44.722338Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T17:50:44.722338Z digest=sha256:413d5ffe835847048c08c671e035cd84762020d9767ab3c7a9b3f6ca4fa94301

Observation b2d9779a-123b-4fde-84d5-8d7354aa0802 · outbound

This paper cites Polar subcodes,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Polar subcodes,

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.874254Z

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=2026-08-06T17:50:44.724787Z digest=sha256:b2aa8a67bf00490260b9ddbba058f0b710a06f4b5cfa578db0f55218fd556e85

Observation bb8c0c78-432f-42d7-8121-ba0e88c0f8b0 · outbound

This paper cites List Decoding of Arıkan’s PAC Codes,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel List Decoding of Arıkan’s PAC Codes,

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.867626Z

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=2026-08-06T17:50:44.727082Z digest=sha256:e1bed1d309d22f787be6f8c7e019b57dfb6c066f8b420d2dda7b2b67356a6a37

Observation ded4e9cb-59bc-4e09-8240-901f50cdaf53 · outbound

This paper cites Polarization-adjusted convolu- tional (PAC) codes: Sequential decoding vs list decoding,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Polarization-adjusted convolu- tional (PAC) codes: Sequential decoding vs list decoding,

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.861433Z

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=2026-08-06T17:50:44.730937Z digest=sha256:f2e65216805e733c9947d4f423021451c42f3f6d6a607d9ffa65323bafc82106

Observation 98004fca-b98a-4e1e-8c9a-7d87a3b6552d · outbound

This paper cites On Pre-transformed Polar Codes.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel On Pre-transformed Polar Codes

Reference 23

Resolution
verified exact
local_arxiv, observed 2026-08-06T17:50:44.776760Z

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=2026-08-06T17:50:44.733707Z digest=sha256:67a96e63f9939c0a85bb0ddc2791015c2068e554de70ea6d2bc2523f45a8d4ae

Observation 0a580014-5fd2-4d06-bd20-6029a138a767 · outbound

This paper cites On the weight spectrum of pre-transformed polar codes,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel On the weight spectrum of pre-transformed polar codes,

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.852422Z

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=2026-08-06T17:50:44.736945Z digest=sha256:dd0c24c95dcc32badbf9991503227939333af2c6e7c2852fe273c86814694fb9

Observation 34988874-543f-4dcf-9153-460949ea01b5 · outbound

This paper cites On the Minimum Weight Codewords of PAC Codes: The Impact of Pre-Transformation,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel On the Minimum Weight Codewords of PAC Codes: The Impact of Pre-Transformation,

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.845212Z

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=2026-08-06T17:50:44.740027Z digest=sha256:f948e2c551d9cb89b1d1b0f3ba91050c269c329daeb0c43ff4c1ea8ae9b4ede5

Observation 14037b3e-74a1-4e11-a4e2-8b2988da701d · outbound

This paper cites Channel coding rate in the finite blocklength regime,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Channel coding rate in the finite blocklength regime,

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.836823Z

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=2026-08-06T17:50:44.742274Z digest=sha256:bb7364f52651fd977c6678731af1ec005f1eb1233e7e8fb488898bfcfacb111a

Observation c4588b17-69be-4ae1-975f-72b8a4fb5372 · outbound

This paper cites Coding in the Finite-Blocklength Regime: Bounds Based on Laplace Integrals and Their Asymptotic Approximations,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Coding in the Finite-Blocklength Regime: Bounds Based on Laplace Integrals and Their Asymptotic Approximations,

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.829949Z

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=2026-08-06T17:50:44.744490Z digest=sha256:5ae5def9ea5d3d2eb891c72e56a82f8880686f905dff9f8ed9b3392fdf86b156

Observation 6473c0c2-0db1-4f47-9c08-0fd24b472e7b · outbound

This paper cites SPECTRE: Short-Packet Communication Toolbox,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel SPECTRE: Short-Packet Communication Toolbox,

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.822208Z

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=2026-08-06T17:50:44.746923Z digest=sha256:2fbd74ceb4f488df1b6134893e0fc517cf3cc6d3de78caa29fe587ecb8b5b31e

Observation 2d5c7de5-7a47-413a-92c7-802814854610 · outbound

This paper cites Recursive projection-aggregation decoding of Reed- Muller codes,.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel Recursive projection-aggregation decoding of Reed- Muller codes,

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.813047Z

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=2026-08-06T17:50:44.749326Z digest=sha256:779e719e11a1336e7418a81623eeca296e103768256a1f04a10ea792d3d58db6

Observation a7212b00-c7b6-47f6-8b8f-8336a124131e · outbound

This paper cites r1 ≤ mX i=1 Zi ≤ r2 # = P.

BiD Codes: Algebraic Codes from $3 \times 3$ Kernel r1 ≤ mX i=1 Zi ≤ r2 # = P

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T17:50:44.802444Z

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=2026-08-06T17:50:44.752156Z digest=sha256:2ab3b86f4cb89d24e3ca3b983c36eb1061d02cdf168355f6bc59af6afb5e379c

Pith citing papers

No inbound Pith citation observations are available.