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