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arXiv · 2001.05787

Weight Enumerators and Cardinalities for Number-Theoretic Codes

Takayuki Nozaki
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Abstract

The number-theoretic codes are a class of codes defined by single or multiple congruences. These codes are mainly used for correcting insertion and deletion errors, and for correcting asymmetric errors. This paper presents a formula for a generalization of the complete weight enumerator for the number-theoretic codes. This formula allows us to derive the weight enumerators and cardinalities for the number-theoretic codes. As a special case, this paper provides the Hamming weight enumerators and cardinalities of the non-binary Tenengolts' codes, correcting single insertion or deletion. Moreover, we show that the formula deduces the MacWilliams identity for the linear codes over the ring of integers modulo $r$.

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Takayuki Nozaki. 2020-01-16. Weight Enumerators and Cardinalities for Number-Theoretic Codes. https://doi.org/10.1109/tit.2022.3184776

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