New good quasi-cyclic ternary and quaternary linear codes

Abstract

Let [n,k,d;q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). The following quasi-cyclic codes are constructed in this paper: [44,11,20;3], [55,11:26:3], [66,11,32;3], [48,12,21;3], [60,12,28;3], [56,13,24;3], [65,13,29;3], [56,14,23;3], [60,15,23;3], [64,16,25;3], [36,9,19;4], [90,9,55;4], [99,9,61;4], [30,10,14;4], [50,10,27;4], [55,10,30;4], [33,11,15;4], [44,11,22;4], [55,11,29;4], [36,12,16;4], [48,12,23;4], [60,12,31;4]. All of these codes have established or exceed the respective lower bounds on the minimum distance given by Brouwer.