Quasi-MSRD Codes and Their Properties
2026-08-10 • Information Theory
Information Theory
AI summaryⓘ
The authors study a type of error-correcting code called sum-rank-metric codes, which are useful in areas like network communication and data storage. They focus on MSRD codes, which are optimal but not always available for every size. To address this, they introduce a new category called quasi-MSRD (QMSRD) codes and explore their properties. They also define a special kind called dually QMSRD codes, where both the code and its dual share the QMSRD property, and provide detailed characterizations of these codes.
sum-rank-metric codesMSRD codesquasi-MSRD codesdually QMSRD codesSingleton bounddual codesrank-metricgeneralized sum-rank weightssupport distribution
Authors
Qingfeng Xia, Fang-Wei Fu
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.