Pith. sign in

REVIEW 5 cited by

More MDS codes of non-Reed-Solomon type

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2401.03391 v1 pith:DXVRSU2E submitted 2024-01-07 cs.IT math.COmath.IT

Yansheng Wu , Ziling Heng , Chengju Li , Cunsheng Ding This is my paper · ORCID
classification cs.ITmath.COmath.IT
keywords codesalmostadditionallyalgebraicapplicationsapplyingassociatedcapability
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and establish some sufficient and necessary conditions for them being MDS. Notably, these codes differ from Reed-Solomon codes up to monomial equivalence. Additionally, we also explore the cases in which these codes are almost MDS or near MDS. Applying our main results, we determine the covering radii and deep holes of the dual codes associated with specific Roth-Lempel codes and discover an infinite family of (almost) optimally extendable codes with dimension three.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Hermitian Hull Dimensions for a Class of (L,P)-Twisted Generalized Reed-Solomon Codes

    cs.IT 2026-07 accept novelty 6.0 of 10

    Hermitian hull dimensions of the codes C_{q+j}(α) are fully determined in three cases on i and q+1, producing EAQECC parameters [[i(q-1), q-1+m, d, (i-2)(q-1)+m]]_q for m=0,1,2,3.

  2. Efficient Decoding of Twisted GRS Codes and Roth-Lempel Codes

    cs.IT 2025-12 conditional novelty 6.0 of 10

    Twisted GRS and Roth-Lempel codes can be list- and uniquely-decoded in near-linear time by running Guruswami-Sudan on a containing generalized Reed-Solomon code and filtering the output.

  3. On subcodes of the generalized Reed-Solomon codes

    cs.IT 2025-07 conditional novelty 6.0 of 10

    It characterizes self-duality and near-MDS status for one-codimensional subcodes of generalized Reed-Solomon codes for all r, and determines the dual codes for r=1,2,k-1.

  4. Row-Column Twisted Reed-Solomon codes

    cs.IT 2025-09 conditional novelty 5.0 of 10

    A new family of maximum-distance-separable codes, RCTRS, is built by applying row and column twists to Reed-Solomon codes and is claimed to be inequivalent to both RS and column-twisted RS codes.

  5. Some constructions of non-generalized Reed-Solomon MDS Codes

    cs.IT 2025-06 conditional novelty 5.0 of 10

    Necessary and sufficient conditions are given for two extended evaluation-code families to be non-GRS MDS codes, and o-monomials are characterized by nonvanishing complete symmetric functions.

Pith tools