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Quasi-cyclic codes over Z4 and some new binary codes

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2 Author(s)
Aydin, N. ; Dept. of Math., Ohio State Univ., Columbus, OH, USA ; Ray-Chaudhuri, D.K.

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

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 7 )