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

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 $3$.

arXiv comment12 pages, 21 references, the reference [6] is corrected

Cited by in corpus (1)

• On cosets weight distributions of the doubly-extended Reed-Solomon codes of codimension 4