Quasi-cyclic codes: algebraic properties and applications

Abstract

In this paper, we provide criteria for the reversibility and conjugate-reversibility of 1-generator quasi-cyclic codes. The Chinese remainder theorem is used to provide a characterization for generalized quasi-cyclic codes to be Galois linear complementary-dual and Galois self-dual. Using the approach proposed by Guneri and Ozbudak (IEEE Trans Inf Theory 59(2):979–985, 2013), a new concatenated structure for quasi-cyclic codes is given. We show that Galois linear complementary-dual quasi-cyclic codes are asymptotically good over some finite fields. In addition, DNA codes are given which have more codewords than previously known codes.