New Binary Quantum Codes Constructed from Quasi-Cyclic Codes

Six new binary quasi-cyclic codes

Six new quasi-cyclic codes are presented, which improve the lower bounds on the minimum distance for a binary code. A local exhaustive search is used to find these codes and many other quasi-cyclic codes which attain the lower bounds.

Quasi-cyclic codes over Z4 and some new binary codes

Recently, (linear) codes over and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study -QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to produces a new binary code, a (92 2 28)-code, which is the best among all binary codes (linear or nonlinear). ...

S-Boxes from Binary Quasi-Cyclic Codes

New Quantum MDS codes constructed from Constacyclic codes

Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form q = 2am + t, n = q 2 +1 a . Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.

On the binary quasi-cyclic codes

In this paper we present a description of quasi-cyclic codes which relies on matrices and gives an efficient algorithm for their construction.