Vol. 13, No. 1, 2020

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Some generalizations of the ASR search algorithm for quasitwisted codes

Nuh Aydin, Thomas H. Guidotti, Peihan Liu, Armiya S. Shaikh and Robert O. VandenBerg

Vol. 13 (2020), No. 1, 137–148
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 𝔽5. 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.

Keywords
quasitwisted codes, multitwisted codes, best known linear codes, ASR search algorithm
Mathematical Subject Classification 2010
Primary: 94B15, 94B60
Milestones
Received: 2 August 2019
Revised: 8 December 2019
Accepted: 27 December 2019
Published: 4 February 2020

Communicated by Kenneth S. Berenhaut
Authors
Nuh Aydin
Kenyon College
Gambier, OH
United States
Thomas H. Guidotti
Kenyon College
Gambier, OH
United States
Peihan Liu
Kenyon College
Gambier, OH
United States
Armiya S. Shaikh
Kenyon College
Gambier, OH
United States
Robert O. VandenBerg
Kenyon College
Gambier, OH
United States