Weight Enumerators and Cardinalities for Number-Theoretic Codes
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 .
Keywords
Cite
@article{arxiv.2001.05787,
title = {Weight Enumerators and Cardinalities for Number-Theoretic Codes},
author = {Takayuki Nozaki},
journal= {arXiv preprint arXiv:2001.05787},
year = {2022}
}
Comments
9 pages, accepted to IEEE Transactions on Information Theory