Fq-Linear Cyclic Codes over Fq: DFT Characterization
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the algebraic structure of quasi-cyclic codes .I. Finite fields
IEEE Transactions on Information Theory
Provably good codes for hash function design
IEEE Transactions on Information Theory
Provably good codes for hash function design
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Skew quasi-cyclic codes over Galois rings
Designs, Codes and Cryptography
Constructing quasi-cyclic codes from linear algebra theory
Designs, Codes and Cryptography
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Quasicyclic codes of length n = ml and index l over the finite field Fq are linear codes invariant under cyclic shifts by l places. They are shown to be isomorphic to the Fq[x]/ 〈xm - 1〉-submodules of Fql[x]/ 〈xm - 1〉 where the defining property in this setting is closure under multiplication by x with reduction modulo xm - 1. Using this representation, the dimension of a 1-generator code can be determined straightforwardly from the chosen generator, and improved lower bounds on minimum distance are developed. A special case of multigenerator codes, for which the dimension can be algebraically recovered from the generating set is described. Every possible dimension of a quasicyclic code can be obtained in some such special form. Lower bounds on minimum distance are also given for all multi-generator quasicyclic codes.