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The Structure of 1-Generator Quasi-Twisted Codes and New Linear Codes

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Abstract

One of the most important problems of coding theory is to construct codes with best possible minimum distances. Recently, quasi-cyclic (QC) codes have been proven to contain many such codes. In this paper, we consider quasi-twisted (QT) codes, which are generalizations of QC codes, and their structural properties and obtain new codes which improve minimum distances of best known linear codes over the finite fields GF(3) and GF(5). Moreover, we give a BCH-type bound on minimum distance for QT codes and give a sufficient condition for a QT code to be equivalent to a QC code.

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Authors
  1. Nuh Aydin
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  2. Irfan Siap
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  3. Dijen K. Ray-Chaudhuri
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Aydin, N., Siap, I. & Ray-Chaudhuri, D.K. The Structure of 1-Generator Quasi-Twisted Codes and New Linear Codes. Designs, Codes and Cryptography 24, 313–326 (2001). https://doi.org/10.1023/A:1011283523000

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  • DOI: https://doi.org/10.1023/A:1011283523000