Concatenated Sum-Rank Codes

Huimin Lao; Hao Chen; San Ling; Yaqi Chen

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arXiv · 2602.21609

Concatenated Sum-Rank Codes

Huimin Lao·Hao Chen·San Ling·Yaqi Chen

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Abstract

Sum-rank codes have wide applications in multishot network coding, distributed storage and the construction of space-time codes. Asymptotically good sequences of linearized algebraic geometry sum-rank codes, exceeding the Gilbert-Varshamov-like bound, were constructed in a recent paper published in IEEE Trans. Inf. Theory by E. Berardini and X. Caruso. We call this bound the Tsfasman-Vladut-Zink-like bound. In this paper, we introduce the concatenation of a sum-rank code and a Hamming metric code. Then many sum-rank codes with good parameters, which are better than sum-rank BCH codes, are constructed simply and explicitly. Moreover, we obtain an asymptotically good sequence of sum-rank codes exceeding the Tsfasman-Vladut-Zink-like bound and the Gilbert-Varshamov-like bound.

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Huimin Lao, Hao Chen, San Ling, Yaqi Chen. 2026-02-25. Concatenated Sum-Rank Codes. https://arxiv.org/abs/2602.21609

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