On the Algebraic Structure of Quasi-Cyclic Codes III: Generator Theory
- 27 June 2005
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 51 (7) , 2692-2700
- https://doi.org/10.1109/tit.2005.850142
Abstract
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.Keywords
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