Title :
Quasi-cyclic codes over Z4 and some new binary codes
Author :
Aydin, Nuh ; Ray-Chaudhuri, Dwijendra K.
Author_Institution :
Dept. of Math., Ohio State Univ., Columbus, OH, USA
fDate :
7/1/2002 12:00:00 AM
Abstract :
Previously, (linear) codes over Z4 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 Z4 produces a new binary code, a (92, 224, 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
Keywords :
Galois fields; binary codes; cyclic codes; linear codes; nonlinear codes; polynomials; Galois field; Golay code; Gray map; Z4-QC codes; binary codes; coding theory; cyclic codes; finite fields; free modules; generator polynomials; linear codes; nonlinear codes; quasi-cyclic codes; Binary codes; Galois fields; Linear code; Mathematics; Web sites;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2002.1013145
