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 introduce a class of dualcontaining 2 -generator quasi-cyclic codes over
GF(4). By Hermitian construction, we show computation constructions of binary quantum codes with good parameters from quaternary quasi-cyclic codes. Furthermore, 3 new quantum codes [[42, 10, 9]], [[74,,36, 9]] and [[78, 40, 9]] are derived from Hermitian dual-containing quasi-cyclic codes by an exhaustive search, along with 24 newly derived codes that enhance the previously best-known lower bounds on minimum distance.