Quasi-cyclic codes over Z/sub 4/ and some new binary codes

Abstract

Previously, (linear) codes over Z/sub 4/ and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z/sub 4/-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z/sub 4/ produces a new binary code, a (92, 2/sup 24/, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials.