New Explicit Good Linear Sum-Rank-Metric Codes

Abstract

Sum-rank-metric codes have wide applications in such as universal error correction and security in multishot network, space-time coding and construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric codes have been studied and some explicit or probabilistic constructions of good sumrank-metric codes have been proposed. In this paper we propose two simple constructions of explicit linear sum-rank-metric codes. In finite length regime, numerous good linear sum-rank-metric codes from our construction are given. Some of them have better parameters than previous constructed sum-rank-metric codes. For example a lot of small block size better linear sum-rank-metric codes over F q of the matrix size 2 × 2 are constructed for q = 2, 3, 4. Asymptotically our constructed sum-rank-metric codes are closing to the Gilbert-Varshamovlike bound for the sum-rank-metric codes for some parameters.