Designs, Codes and Cryptography

, Volume 24, Issue 3, pp 313-326

First online:

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

  • Nuh Aydin
  • , Irfan Siap
  • , Dijen K. Ray-Chaudhuri

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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.

quasi-twisted codes new bounds ternary codes