Near MDS poset codes and distributions

Alexander Barg; Punarbasu Purkayastha

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arXiv · 1004.5601

Near MDS poset codes and distributions

Alexander Barg·Punarbasu Purkayastha

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Abstract

We study $q$-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works. We consider codes that are close to MDS codes by the value of their minimum distance. For such codes, we determine their weight distribution, and in the particular case of the "ordered metric" characterize distributions of points in the unit cube defined by the codes. We also give some constructions of codes in the ordered Hamming space.

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Alexander Barg, Punarbasu Purkayastha. 2010-04-30. Near MDS poset codes and distributions. https://arxiv.org/abs/1004.5601

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