On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
Treillis de codes quasi-cycliques
European Journal of Combinatorics - Special issue on arithmétique et combinatoire
Fq-linear cyclic codes over Fqm: DFT approach
Designs, Codes and Cryptography
On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots
Designs, Codes and Cryptography
Cyclic Codes Over$$\mathbb{Z}_{4}$$ of Even Length
Designs, Codes and Cryptography
On binary self-dual codes of lengths 60, 62, 64 and 66 having an automorphism of order 9
Designs, Codes and Cryptography
Discrete Applied Mathematics
On self-orthogonal group ring codes
Designs, Codes and Cryptography
Construction of cubic self-dual codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
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
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
Spectral graph analysis of quasi-cyclic codes
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
On the construction of skew quasi-cyclic codes
IEEE Transactions on Information Theory
Quaternary 1-generator quasi-cyclic codes
Designs, Codes and Cryptography
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
Designs, Codes and Cryptography
Quasi-cyclic codes with cyclic constituent codes
Finite Fields and Their Applications
Quasi-cyclic codes as codes over rings of matrices
Finite Fields and Their Applications
On complementary-dual quasi-cyclic codes
Finite Fields and Their Applications
Constructing quasi-cyclic codes from linear algebra theory
Designs, Codes and Cryptography
Trace representation of quasi-negacyclic codes
BICS'13 Proceedings of the 6th international conference on Advances in Brain Inspired Cognitive Systems
Supersingular curves over finite fields and weight divisibility of codes
Journal of Computational and Applied Mathematics
Matrix product codes over finite commutative Frobenius rings
Designs, Codes and Cryptography
| Hi-index | 754.90 |
A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese remainder theorem (CRT), or of the discrete Fourier transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the (u+υ|u-υ) and Vandermonde constructions. All binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction. Quinting and septing constructions are introduced. Other results made possible by the ring decomposition are a characterization of self-dual quasi-cyclic codes, and a trace representation that generalizes that of cyclic codes