1. Weight Enumerators and Cardinalities for Number-Theoretic Codes.
- Author
-
Nozaki, Takayuki
- Subjects
HAMMING weight ,RINGS of integers ,BINARY codes ,LINEAR codes ,ERROR-correcting codes - Abstract
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 $r$. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF