Integer sequences that are generalized weights of a linear code
Information Theory
2023-07-14 v1 math.IT
Abstract
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally for sum-rank metric codes. We do so under an existence assumption for MDS and MSRD codes. We also prove that the same integer sequences appear as sequences of greedy weights of linear block codes, rank-metric codes, and sum-rank metric codes. Finally, we characterize the integer sequences which appear as sequences of relative generalized weights (respectively, relative greedy weights) of linear block codes.
Keywords
Cite
@article{arxiv.2307.06595,
title = {Integer sequences that are generalized weights of a linear code},
author = {Elisa Gorla and Elisa Lorenzo García and Umberto Martínez-Peñas and Flavio Salizzoni},
journal= {arXiv preprint arXiv:2307.06595},
year = {2023}
}
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19 pages