Skew-cyclic codes

被引：194

作者：

Boucher, D.

Geiselmann, W.

Ulmer, F.

机构：

[1] Univ Rennes 1, IRMAR, F-35042 Rennes, France

[2] Univ Karlsruhe, Fak Informat, IAKS, D-76128 Karlsruhe, Germany

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2007年 / 18卷 / 04期

关键词：

cyclic codes; finite rings;

D O I：

10.1007/s00200-007-0043-z

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since there are much more skew-cyclic codes, this new class of codes allows to systematically search for codes with good properties. We give many examples of codes which improve the previously best known linear codes.

引用

页码：379 / 389

页数：11

共 8 条

[1]

[Anonymous], 1989, INTRO ERROR CORRECTI

[2] The Magma algebra system .1. The user language [J].

Bosma, W ;

Cannon, J ;

Playoust, C .

JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265

[3]

BROUWER AE, 2005, SERVER BOUNDS MINIMU

[4]

Gabidulin E.M., 1985, PROBL PEREDACHI INF, V21, P3

[5]

MACWILLIAMS FJ, 1981, THEORY ERROR CORRECT

[6]

McDonald B.R., 1974, Pure and Applied Mathematics

[7] Theory of non-commutative polynomials [J].

Ore, O .

ANNALS OF MATHEMATICS, 1933, 34 :480-508

[8]

SENDRIER N, THESIS U PARIS 6

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