Quasi-MSRD Codes and Their Properties

Qingfeng Xia; Fang-Wei Fu

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arXiv · 2608.09085

Quasi-MSRD Codes and Their Properties

Qingfeng Xia·Fang-Wei Fu

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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.

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Qingfeng Xia, Fang-Wei Fu. 2026-08-10. Quasi-MSRD Codes and Their Properties. https://arxiv.org/abs/2608.09085

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