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Technical Program

Paper Detail

Paper IDD1-S5-T2.3
Paper Title Distance Enumerators for Number-Theoretic Codes
Authors Takayuki Nozaki, Yamaguchi University, Japan
Session D1-S5-T2: Distance Metrics
Chaired Session: Monday, 12 July, 23:20 - 23:40
Engagement Session: Monday, 12 July, 23:40 - 00:00
Abstract The number-theoretic codes are a class of codes defined by single or multiple congruences and are mainly used for correcting insertion and deletion errors. Since the number-theoretic codes are generally non-linear, the analysis method for such codes is not established enough. The distance enumerator of a code is a unary polynomial whose ith coefficient gives the number of the pairs of codewords with distance i. The distance enumerator gives the maximum likelihood decoding error probability of the code. This paper presents an identity of the distance enumerators for the number-theoretic codes. Moreover, as an example, we derive the Hamming distance enumerator for the Varshamov-Tenengolts (VT) codes.