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Sum-rank metric codes
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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.
Forward citations
Cited by 3 Pith papers
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On the Etzion-Silberstein conjecture for block Ferrers diagrams
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.
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Function-Correcting Codes for Sum-Rank Metric
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.
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On the non-existence of perfect codes in the sum-rank metric
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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