Concatenated Sum-Rank Codes
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.
Cite
@article{arxiv.2602.21609,
title = {Concatenated Sum-Rank Codes},
author = {Huimin Lao and Hao Chen and San Ling and Yaqi Chen},
journal= {arXiv preprint arXiv:2602.21609},
year = {2026}
}