2011/08/18 by Barbier, Morgan, Chabot, Christophe, Quintin, Guillaume
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1108.3754
In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic codes of length m and ideals of Ml(Fq)[X]/(Xm-1). This permits to construct new classes of codes, namely quasi-BCH and quasi-evaluation codes. We study the parameters of such codes and propose a decoding algorithm up to half the designed minimum distance. We even found one new quasi-cyclic code with better parameters than known [189, 11, 125]F4 and 48 derivated codes beating the known bounds as well.