On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots
Designs, Codes and Cryptography
On self-orthogonal group ring codes
Designs, Codes and Cryptography
Provably good codes for hash function design
IEEE Transactions on Information Theory
Construction of cubic self-dual codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
On quasi-cyclic codes over integer residue rings
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Structural properties and enumeration of 1-generator generalized quasi-cyclic codes
Designs, Codes and Cryptography
Skew quasi-cyclic codes over Galois rings
Designs, Codes and Cryptography
On complementary-dual quasi-cyclic codes
Finite Fields and Their Applications
Constructing quasi-cyclic codes from linear algebra theory
Designs, Codes and Cryptography
| Hi-index | 754.90 |
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.