New Explicit Good Linear Sum-Rank-Metric Codes

Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the construction of partial-MDS for repair distributed storage. Fundamental properties sum-rank-metric been studied some explicit or probabilistic constructions good proposed. In this paper we give three simple linear codes. finite length regime, numerous larger with same minimum sum-rank distances as previous constructed can be derived from our constructions. For example several better over F q small block sizes matrix size 2 × are q = 2, 3,4 by applying to presently known best Asymptotically close Gilbert-Varshamov-like bound on parameters. Finally construct a MSRD code an arbitrary field various square xmlns:xlink="http://www.w3.org/1999/xlink">n xmlns:xlink="http://www.w3.org/1999/xlink">1 , xmlns:xlink="http://www.w3.org/1999/xlink">2 ,..., xmlns:xlink="http://www.w3.org/1999/xlink">nt satisfying xmlns:xlink="http://www.w3.org/1999/xlink">ni ≥ 2 xmlns:xlink="http://www.w3.org/1999/xlink">i+1 + · xmlns:xlink="http://www.w3.org/1999/xlink">t xmlns:xlink="http://www.w3.org/1999/xlink">i 1,2,..., xmlns:xlink="http://www.w3.org/1999/xlink">t — 1, any given distance. There is no restriction lengths parameters xmlns:xlink="http://www.w3.org/1999/xlink">N these fields .