Distance Enumerators for Number-Theoretic Codes
Takayuki Nozaki

TL;DR
This paper introduces a new identity for the distance enumerator of number-theoretic codes, facilitating analysis of their error correction capabilities, and exemplifies this with the Hamming distance enumerator for VT codes.
Contribution
It establishes an identity for the distance enumerator of number-theoretic codes and derives the Hamming distance enumerator for VT codes as an example.
Findings
Derived the distance enumerator identity for number-theoretic codes
Calculated the Hamming distance enumerator for VT codes
Enhanced understanding of error correction analysis for these codes
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 th coefficient gives the number of the pairs of codewords with distance . 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.
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Taxonomy
TopicsDNA and Biological Computing · Coding theory and cryptography · Algorithms and Data Compression
