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Applicable Algebra in Engineering, Communication and Computing

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17-05-2017 | Original Paper

New binary linear codes from quasi-cyclic codes and an augmentation algorithm

Authors: Nuh Aydin, Nicholas Connolly, John Murphree

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 4/2017

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Abstract

Explicit construction of linear codes with best possible parameters is one of the major problems in coding theory. Among all alphabets of interest, the binary alphabet is the most important one. In this work we use a comprehensive search strategy to find new binary linear codes in the well-known and intensively studied class of quasi-cyclic (QC) codes. We also introduce a generalization of an augmentation algorithm to obtain further new codes from those QC codes. Also applying the standard methods of obtaining new codes from existing codes, such as puncturing, extending and shortening, we have found a total of 62 new binary linear codes.

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Title: New binary linear codes from quasi-cyclic codes and an augmentation algorithm
Authors: Nuh Aydin
Nicholas Connolly
John Murphree
Publication date: 17-05-2017
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 4/2017
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-017-0327-x

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