Noah Aydin, Professor of Mathematics, has published an article, “A new algorithm for equivalence of cyclic codes and its applications,” (Sept 2021) with R. Oliver VandenBerg ’20 in Applicable Algebra in Engineering Communication and Computing journal.
What is a cyclic code? A cyclic code is a block code in coding theory, where the circular shifts of each codeword gives another word that belongs to the code. These are error-correcting codes that have algebraic properties which are convenient for efficient error detection and correction.
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems related to cyclic codes. In this work, we use recent results on the equivalence of cyclic codes to create a more efficient algorithm to partition cyclic codes by equivalence based on cyclotomic cosets. This algorithm is then implemented to carry out computer searches for both cyclic codes and quasi-cyclic (QC) codes with good parameters. We also generalize these results to repeated-root cases. We have found several new linear codes that are cyclic or QC as an application of the new approach, as well as more desirable constructions for linear codes with best known parameters. With the additional new codes obtained through standard constructions, we have found a total of 14 new linear codes.