Some generalizations of the ASR search algorithm for quasitwisted codes

Abstract

One of the most important and challenging problems in coding theory is explicit construction of linear codes with the best possible parameters. It is well known that the class of quasitwisted (QT) codes is asymptotically good and contains many linear codes with best known parameters (BKLCs). A search algorithm (ASR) on QT codes has been particularly effective to construct such codes. Recently, the ASR algorithm was generalized based on the notion of code equivalence. In this work, we introduce a new generalization of the ASR algorithm to include a broader scope of QT codes. As a result of implementing this algorithm, we have found eight new linear codes over the field ${\mathbb{𝔽}}_5$. Furthermore, we have found seven additional new codes from the standard constructions of puncturing, shortening or Construction X. We also introduce a new search algorithm that can be viewed as a further generalization of ASR into the class multitwisted (MT) codes. Using this method, we have found many codes with best known parameters with more direct and desirable constructions than what is currently available in the database of BKLCs.