S-Boxes from Binary Quasi-Cyclic Codes

S-Boxes from Binary Quasi-Cyclic Codes

S - boxes from binary quasi - cyclic codes 1

In this paper we present a construction for S-boxes using quasi-cyclic codes. We obtain S-boxes with good nonlinearity.

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.

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.

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). ...