论文标题
重量枚举者和针对数字理论代码的红衣主教
Weight Enumerators and Cardinalities for Number-Theoretic Codes
论文作者
论文摘要
数字理论代码是由单个或多个一致性定义的一类代码。这些代码主要用于纠正插入和删除错误，并用于纠正不对称误差。本文提出了用于对数字理论代码的完整权重枚举概述的公式。该公式使我们能够为数字理论代码得出重量枚举和红衣主义。作为一种特殊情况，本文提供了非二进制tenengolts代码的锤子重量枚举和红衣，纠正了单个插入或删除。此外，我们证明了公式在整数Modulo $ r $的环上推论MacWilliams的身份。
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 $r$.
