The weight distribution of codes over finite chain rings
Giulia Cavicchioni, Alessio Meneghetti
TL;DR
This paper derives new linear equations for the weight distribution of linear codes over finite chain rings, enabling the computation of full weight distributions for codes with small Singleton defects like MDS, MDR, and AMDR codes.
Contribution
It introduces novel linear identities based on submatrix counts of the parity-check matrix, advancing the analysis of code weight distributions over finite chain rings.
Findings
Derived new linear equations for weight distribution
Computed full weight distributions for MDS, MDR, and AMDR codes
Enhanced understanding of code structures over finite chain rings
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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Taxonomy
TopicsCoding theory and cryptography · Islamic Finance and Communication · Error Correcting Code Techniques