Mohammed Sabiri
ABSTRACT
Quasi-cyclic codes over a finite commutative ring are viewed as cyclic codes over a noncommutative ring of matrices over a finite commutative ring. The study of these codes permits to generalize some known results about quasi-cyclic codes over a finite fields and to propose a construction of some quasi-cyclic codes.
- C. J. L. 1. Quasi-cyclic codes with cyclic constituent codes. Finite Fields and Their Applications., 13:229--254, 2007. Google Scholar
Digital Library
- N. AYDIN and I. SIAP. New quasi-cyclic codes over f5. Applied Mathematics Letters., 15:833--836, 2002.Google ScholarCross Ref
- M. Hazewinkel. Handbook of Algebra, Volume 5. North Holland, 2008.Google Scholar
- A. Necer. Systèmes récursifs et algèbre de hadamard de suites récurrentes linéaires sur des anneaux commutatifs. Communications in Algabra., 15(5):6175--6189, 1999.Google ScholarCross Ref
- A. Nechaev. Finite quasi-frobenius modules, applications to codes and linear recurrences. Fundam. Prikl. Mat., 16(1):229--254, 1995.Google Scholar
- H. Niederreiter. The multiple-recursive matrix method for pseudorandom number generation. Finite Fields and their Applications., 1:3--30, 1995. Google ScholarDigital Library
- A. N. Pierre-Louis Cayrel, Christophe Chabot. Quasi-cyclic codes as codes over rings of matrices. Finite fields and their applications., 16:100--115, 2010. Google ScholarDigital Library
- P. S. S. Ling. Decomposing quasi-cyclic codes. In International Workshop on Coding and Cryptography, pages 8--12, January 2001.Google ScholarCross Ref
- P. S. S. Ling. On the algebraic structure of quasi-cyclic codes i: finite fields. IEEE Trans., 16(47):2751--2760, 2001. Google ScholarDigital Library
- A. V. M. A. A. N. V. L. Kurakin, A. S. Kuzmin. Linear recurring sequences over rings and modules. Journal of Mathematical Sciences, 76(6):2793--2915, 10 1995.Google ScholarCross Ref
- J. L. Walker. Algebraic geometric codes over rings. Journal of Pure and Applied Algebra., 144:99--110, 1999.Google ScholarCross Ref
- F. M. Williams and N. J. A. Sloane. The theory of error-corecting codes. Mathematical Library, North-Holland, 1981.Google Scholar
Recommendations
Quasi-cyclic codes as codes over rings of matrices
Quasi-cyclic codes over a finite field are viewed as cyclic codes over a noncommutative ring of matrices over a finite field. This point of view permits to generalize some known results about linear recurring sequences and to propose a new construction ...
Quasi-cyclic codes as cyclic codes over a family of local rings
We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the ...
On quasi-cyclic codes over integer residue rings
AAECC'07: Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codesIn this paper we consider some properties of quasi-cyclic codes over the integer residue rings. A quasi-cyclic code over Zk, the ring of integers modulo k, reduces to a direct product of quasi-cyclic codes over Zpi ei, k = &Pi:i = 1s piei, pi, a prime. ...
Comments