On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
Repeated-root cyclic and negacyclic codes over a finite chain ring
Discrete Applied Mathematics - Special issue: Coding and cryptography
Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2
Designs, Codes and Cryptography
Quasicyclic codes of index l over Fq viewed as Fq[x]-submodules of Fql[x]/ċ xmċ1ċ
AAECC'03 Proceedings of the 15th 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
Cyclic codes and self-dual codes over F2+uF2
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes .I. Finite fields
IEEE Transactions on Information Theory
Decoding of circulant codes (Corresp.)
IEEE Transactions on Information Theory
A Gilbert-Varshamov bound for quasi-cycle codes of rate 1/2 (Corresp.)
IEEE Transactions on Information Theory
Cyclic and negacyclic codes over finite chain rings
IEEE Transactions on Information Theory
On the algebraic structure of quasi-cyclic codes III: generator theory
IEEE Transactions on Information Theory
Quasi-cyclic codes as codes over rings of matrices
Finite Fields and Their Applications
The Multiple-Recursive Matrix Method for Pseudorandom Number Generation
Finite Fields and Their Applications
Trace representation of quasi-negacyclic codes
BICS'13 Proceedings of the 6th international conference on Advances in Brain Inspired Cognitive Systems
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Let F q be a finite field of cardinality q, l and m be positive integers and M l (F q ) the F q -algebra of all l 脳 l matrices over F q . We investigate the relationship between monic factors of X m 驴 1 in the polynomial ring M l (F q )[X] and quasi-cyclic (QC) codes of length lm and index l over F q . Then we consider the idea of constructing QC codes from monic factors of X m 驴 1 in polynomial rings over F q -subalgebras of M l (F q ). This idea includes ideas of constructing QC codes of length lm and index l over F q from cyclic codes of length m over a finite field F q l, the finite chain ring F q + uF q + · · · + u l 驴 1 F q (u l = 0) and other type of finite chain rings.