Constructions of Codes in the Sum-Rank Metric

Coding Theory and Cryptography Seminars

The sum-rank metric simultaneously extends the Hamming metric and the rank metric. Thus it provides a general theory that includes both classical and rank-metric codes. In this talk, we will present several constructions of Maximum Sum-Rank Distance (MSRD) codes. Each of these codes outperforms all possible MRD codes in the applications, as they require polynomial field sizes (in contrast with exponential field sizes for MRD codes). Our constructions include our previous construction of linearized Reed-Solomon codes, which simultaneously generalize Reed-Solomon codes and Gabidulin codes. At the end, we will present Sum-Rank BCH codes, a family of subfield subcodes of linearized Reed-Solomon codes with small field sizes and good parameters, and which extend classical BCH codes.