On equivalence of cyclic codes, generalization of a quasi-twisted search algorithm, and new linear codes

• Published in: Designs, codes, and cryptography Vol. 87; no. 10; pp. 2199 - 2212
• Main Authors: Aydin, Nuh, Lambrinos, Jonathan, VandenBerg, Oliver
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2019; Springer Nature B.V
• Subjects: Algorithms; Binary system; Circuits; Codes; Coding and Information Theory; Computer Science; Cryptology; Data Structures and Information Theory; Discrete Mathematics in Computer Science; Equivalence; Information and Communication; Linear codes; Search algorithms; 94B15; Constacyclic codes; Search algorithms for linear codes; 94B05; Best known linear codes; Cyclic codes; Equivalence of codes; Quasi-twisted codes
• ISSN: 0925-1022; 1573-7586
• DOI: 10.1007/s10623-019-00613-0

A fundamental problem in coding theory is the explicit construction of linear codes with best possible parameters. A search algorithm (ASR) on certain types of quasi-twisted (QT) codes has been very fruitful to address this challenging problem. In this work, we generalize the ASR algorithm to make it more comprehensive. The generalization is based on code equivalence. As a result of implementing the more general algorithm, we discovered 27 new linear codes over the fields F q for q = 3 , 4 , 5 , and 7. Further, we prove several useful theoretical results about the equivalence of cyclic codes, constacyclic codes, and QT codes.