The weight distribution of codes over finite chain rings

Giulia Cavicchioni; Alessio Meneghetti

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arXiv · 2210.15436

The weight distribution of codes over finite chain rings

Giulia Cavicchioni·Alessio Meneghetti

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Abstract

In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code. Thanks to these relations we are able to compute the full weight distribution of codes with small Singleton defects, such as MDS, MDR and AMDR codes.

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Giulia Cavicchioni, Alessio Meneghetti. 2022-10-28. The weight distribution of codes over finite chain rings. https://arxiv.org/abs/2210.15436

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