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arXiv · 2007.02405

On integral weight spectra of the MDS codes cosets of weight 1, 2, and 3

Alexander A. Davydov·Stefano Marcugini·Fernanda Pambianco
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Abstract

The weight of a coset of a code is the smallest Hamming weight of any vector in the coset. For a linear code of length $n$, we call integral weight spectrum the overall numbers of weight $w$ vectors, $0\le w\le n$, in all the cosets of a fixed weight. For maximum distance separable (MDS) codes, we obtained new convenient formulas of integral weight spectra of cosets of weight 1 and 2. Also, we give the spectra for the weight 3 cosets of MDS codes with minimum distance $5$ and covering radius $3$.

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Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco. 2020-07-15. On integral weight spectra of the MDS codes cosets of weight 1, 2, and 3. https://arxiv.org/abs/2007.02405

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