On the binary 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.

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Good Quasi-Cyclic Codes Derived From Irreducible Cyclic Codes

As a generalization of cyclic codes, quasi-cyclic codes contain many good linear codes. Extensive search is made and lots of good quasi-cyclic codes are obtained from irreducible cyclic codes. A new binary [95, 13, 40] code which improves the lower bound on the minimum distance, is also constructed. Index Term — Codes and coding, linear codes, cyclic codes, idempotent, irreducible codes, quasi-...

Some Good Cyclic and Quasi-Twisted Z4-Linear Codes

For over a decade, there has been considerable research on codes over Z4 and other rings. In spite of this, no tables or databases exist for codes over Z4, as is the case with codes over finite fields. The purpose of this work is to contribute to the creation of such a database. We consider cyclic, negacyclic and quasi-twisted (QT) codes over Z4. Some of these codes have binary images with bett...

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). ...