Twelve new binary quasi-cyclic codes, which improve the lower bounds on minimum distances for binary linear codes, are presented, and a Web database on best-known binary quasi-cyclic codes is constructed for public access.
It has been well-known that the class of quasi-cyclic (QC) codes contain many good codes. In this paper, a method to conduct a computer search for binary 2-generator QC codes is presented, and a large number of good 2-generator QC codes have been obtained. 5 new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new 2-generator QC codes and Construction X, 2 new improved binary linear codes are obtained. With the standard construction techniques, another 16 new binary linear codes that improve the lower bound on the minimum distance have also been obtained. Received: 9 November 2016 Accepted: 22 November 2017
In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner product. As the computational results, five new binary quantum codes with parameters [[45,29,5]], [[63,36,7]], [[73,55,5]], [[105,71,7]], and [[105,72,7]] improving the best-known lower bounds on minimum distance in Grassl's code tables are constructed.