Quasi-cyclic codes over Z(4) and some new binary codes
Recently, (linear) codes over 24 and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z(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(4) produces a new binary code, a (92, 2(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.
quasi-cyclic (qc) codes gray map z(4) codes