Quasi-MSRD Codes and Their Properties

Abstract

Sum-rank-metric codes have recently attracted considerable attention of many researchers, due to their applications in network coding, space-time codes and distributed storage. MSRD codes are those good codes attaining the Singleton bound in the sum-rank metric. However, MSRD codes do not exist for some dimensions. Motivated by this fact, we introduce the notion of quasi-MSRD (QMSRD) codes and provide some properties of them. What is more, we find that not every QMSRD code has a QMSRD dual code, so we give the definition of dually QMSRD codes, whose dual codes and themselves are both QMSRD. Finally, we characterize such codes, derive their support, rank-list and sum-rank distributions as well as compute their generalized sum-rank weights.