MDS Convolutional Codes Over a Finite Ring

被引：12

作者：

El Oued, Mohammed ^{[1
]}

Sole, Patrick ^{[2
,3
]}

机构：

[1] Univ Monastir, FSM Math Dept, Monastir 5050, Tunisia

[2] Telecom ParisTech, LTCI, CNRS, F-75634 Paris 13, France

[3] King Abdulaziz Univ, Dept Math, Jeddah 22254, Saudi Arabia

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2013年 / 59卷 / 11期

关键词：

Convolutional codes; cyclic codes; MDS codes; CHAIN RING; CONSTRUCTIONS; DISTANCE;

D O I：

10.1109/TIT.2013.2277721

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we present an analog of the Singleton bound for convolutional codes over finite rings. Codes meeting that bound are called MDS. A constructive method for the MDS codes, restricted to free codes, is presented via cyclic codes over finite rings. Examples of nonfree MDS codes are provided.

引用

页码：7305 / 7313

页数：9

共 15 条

[1] System-theoretic properties of convolutional codes over rings [J].

Fagnani, F ;

Zampieri, S .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (06) :2256-2274

[2] Some structural properties of convolutional codes over rings [J].

Johannesson, R ;

Wan, ZX ;

Wittenmark, E .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (02) :839-845

[3] NEW CONVOLUTIONAL CODE CONSTRUCTIONS AND A CLASS OF ASYMPTOTICALLY GOOD TIME-VARYING CODES [J].

JUSTESEN, J .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1973, 19 (02) :220-225

[4]

Kuijper M, 2008, LECT NOTES COMPUT SC, V5228, P95, DOI 10.1007/978-3-540-87448-5_11

[5] The predictable degree property and row reducedness for systems over a finite ring [J].

Kuijper, Margreta ;

Pinto, Raquel ;

Polderman, Jan Willem .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 425 (2-3) :776-796

[6] On Minimality of Convolutional Ring Encoders [J].

Kuijper, Margreta ;

Pinto, Raquel .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (11) :4890-4897

[7] POLYNOMIAL WEIGHTS AND CODE CONSTRUCTIONS [J].

MASSEY, JL ;

COSTELLO, DJ ;

JUSTESEN, J .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1973, 19 (01) :101-110

[8]

McDonald BR., 1974, Finite Rings with Identity

[9]

McEliece RJ, 1998, HANDBOOK OF CODING THEORY, VOLS I & II, P1065

[10] On the structure of linear and cyclic codes over a finite chain ring [J].

Norton, GH ;

Salagean, A .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2000, 10 (06) :489-506

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