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arXiv · 2601.21121

Periodicity of weight enumerators for codes generated by an integral matrix

Koji Imamura·Norihiro Nakashima·Takuya Saito
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Abstract

In the theory of error-correcting codes, the minimum weight and the weight enumerator play a crucial role in evaluating the error-correcting capacity. In this paper, by viewing the weight enumerator as a quasi-polynomial, we reduce the calculation of the minimum weight to that of a code over a smaller integer residue ring. We also give a transformation formula between the Tutte quasi-polynomial and the weight enumerator. Furthermore, we compute the number of maximum weight codewords for the codes related to the matroids $N_k$ and $Z_k$. This is equivalent to computing the characteristic quasi-polynomial of the hyperplane arrangements related to $N_k$ and $Z_k$.

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Koji Imamura, Norihiro Nakashima, Takuya Saito. 2026-01-28. Periodicity of weight enumerators for codes generated by an integral matrix. https://arxiv.org/abs/2601.21121

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