Repeated-Root Cyclic and Negacyclic Codes of Length 6ps

被引：53

作者：

Dinh, Hai Q. ^{[1
]}

机构：

[1] Kent State Univ, Dept Math Sci, Warren, OH 44483 USA

来源：

RING THEORY AND ITS APPLICATIONS: RING THEORY SESSION IN HONOR OF T.Y. LAM ON HIS 70TH BIRTHDAY | 2014年 / 609卷

关键词：

Cyclic codes; negacyclic codes; constacyclic codes; dual codes; self-dual codes; LCD codes; repeated-root codes; LINEAR CODES;

D O I：

10.1090/conm/609/12150

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p >= 5 be any prime, the structures of cyclic and negacyclic codes of length 6p(s) over the Galois field F(p)m are obtained, in term of specified polynomial generators of such codes. As an application, all self-dual and linear complementary-dual (LCD) cyclic and negacylic codes of length 6p(s) are provided. A classification of all constacyclic codes of length 6p(s) over F(p)m, via ring isomorphisms is given.

引用

页码：69 / 87

页数：19

共 20 条

[1]

Berlekamp E. R., 1984, Algebraic Coding Theory

[2]

Berlekamp ElwynR., 1969, COMBINATORIAL MATH I, P298

[3]

Berman S.D., 1967, Kibernetika, vol, V3, P17

[4] ON REPEATED-ROOT CYCLIC CODES [J].

CASTAGNOLI, G ;

MASSEY, JL ;

SCHOELLER, PA ;

VONSEEMANN, N .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (02) :337-342

[5]

Dinh H.Q., DISCRETE MA IN PRESS

[6] Repeated-root constacyclic codes of length 2ps [J].

Dinh, Hai Q. .

FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (01) :133-143

[7] On complementary-dual quasi-cyclic codes [J].

Esmaeili, M. ;

Yari, S. .

FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (03) :375-386

[8]

Falkner G, 1979, ATTI SEMIN MAT FIS, V28

[9]

Huffman W. C., 2003, FUNDAMENTALS ERROR C

[10]

MacWilliams F., 1998, THEORY ERROR CORRECT

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