Decoding algorithms of monotone codes and azinv codes and their unified view

• Published in: Designs, codes, and cryptography Vol. 90; no. 12; pp. 2893 - 2922
• Main Authors: Takahashi, Hokuto, Hagiwara, Manabu
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2022; Springer Nature B.V
• Subjects: Algorithms; Coding and Information Theory; Computer Science; Cryptology; Decoding; Deletion; Discrete Mathematics in Computer Science; Error correcting codes; Error correction; Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless; Substitutes; Error-correcting codes; Coding theory; 94B50; Decoding algorithm; Insertion/deletion; Balanced adjacent deletion
• ISSN: 0925-1022; 1573-7586
• DOI: 10.1007/s10623-021-01004-0

This paper investigates linear-time decoding algorithms for two classes of error-correcting codes. One of the classes is monotone codes which are known as single deletion error-correcting codes, although they are not known to be single substitution error-correcting codes. The other is azinv codes which are known as single balanced adjacent deletion error-correcting codes, although they are not known to be single balanced adjacent substitution error-correcting codes. As a result, this paper proposes generalizations of Levenshtein’s decoding algorithm for Levenshtein’s single deletion or single substitution error-correcting codes. This paper points out that it is possible to unify our new two decoding algorithms. Moreover, we provide Python implementations of these algorithms and the graphs of their computational costs at https://github.com/Hokuto496/Decoding_Algorithms_of_monotone_codes_and_azinv_codes .