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On the algebraic structure of quasi-cyclic codes III: generator theory

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2 Author(s)

Following Parts I and II, quasi-cyclic codes of given index are studied as codes over a finite polynomial ring. These latter codes are decomposed by the Chinese Remainder Theorem (CRT), or equivalently the Mattson-Solomon transform, into products of shorter codes over larger alphabets. We characterize and enumerate self-dual one-generator quasi-cyclic codes in that context. We give an algorithm to remove some equivalent codes from that enumeration. A generalization to multigenerator codes is sketched.

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Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 7 )