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Sum-rank metric codes

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arxiv 2304.12095 v1 pith:LSFGAN6I submitted 2023-04-24 cs.IT math.IT

classification cs.ITmath.IT
keywords codeslinearmetricsum-rankmathbbtheoryallowedanticodes
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abstract

Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network coding and distributed storage systems. The aim of this chapter is to present the mathematical theory of sum-rank metric codes, paying special attention to the $\mathbb{F}_q$-linear case in which different sizes of matrices are allowed. We provide a comprehensive overview of the main results in the area. In particular, we discuss invariants, optimal anticodes, and MSRD codes. In the last section, we concentrate on $\mathbb{F}_{q^m}$-linear codes.

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Forward citations

Cited by 3 Pith papers

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

  1. On the Etzion-Silberstein conjecture for block Ferrers diagrams

    math.CO 2026-07 accept novelty 6.5 of 10

    MSRD-constructible block Ferrers diagrams attain the Etzion–Silberstein bound over large fields, and reduce to block-triangular cases that yield new arbitrary-field optimal codes for extremal distances.

  2. Function-Correcting Codes for Sum-Rank Metric

    cs.IT 2026-07 accept novelty 6.0 of 10

    Function-correcting sum-rank codes admit a Plotkin-like redundancy bound and achieve optimal redundancy ceil(2t/m) for 2t-locally binary functions via an explicit parity construction.

  3. On the non-existence of perfect codes in the sum-rank metric

    cs.IT 2025-08 conditional novelty 6.0 of 10

    Perfect codes in the sum-rank metric are shown to be impossible for large families of parameters, though the two-block case for small radius and q>e^3 is left unresolved by the proof.

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