Weight Enumerators and Cardinalities for Number-Theoretic Codes
Weight Enumerators and Cardinalities for Number-Theoretic Codes
复制标题
数论代码的权重枚举器和基数
DOI：
10.1109/tit.2022.3184776
复制
发表时间：
2022
影响因子：
2.5
通讯作者：
Nozaki Takayuki
中科院分区：
文献类型：
--
作者：
鈴木月花;中垣好花;木村留美;北川雅恵;長嶺憲太郎;松本顕;Nozaki Takayuki
数论码是由单个或多个同余定义的一类码。这些码主要用于纠正插入和删除错误，以及用于纠正非对称错误。给出了数论码完全重量枚举器的一个推广公式。这个公式允许我们推导出数论代码的重量枚举数和基数。作为特例，给出了纠正单个插入或删除的非二进制Tenengolts码的Hamming重量枚举数和基数。此外，我们还证明了该公式推导出了模整数环上线性码的MacWilliams恒等式。
The number-theoretic code is 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.