CONSTACYCLIC CODES OF LENGTH 8ps OVER Fpm + uFpm

被引：3
作者：
Dinh, H. A. I. Q. [1 ,2 ]
Nguyen, B. A. C. T. [3 ]
Maneejuk, Paravee [4 ]
机构：
[1] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam
[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam
[3] Thai Nguyen Univ Econ & Business Adm, Thai Nguyen, Vietnam
[4] Chiang Mai Univ, Fac Econ, Ctr Excellence Econometr, Chiang Mai, Thailand
来源：
ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2022年 / 16卷 / 03期
关键词：
Constacyclic codes; negacyclic codes; cyclic codes; dual codes; repeated-root codes; chain rings; local rings; NEGACYCLIC CODES; CYCLIC CODES; EXPLICIT REPRESENTATION; Z(4); ENUMERATION; 2P(S); 4P(S);
D O I：
10.3934/amc.2020123
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
For any odd prime p, the structures and duals of lambda-constacyclic codes of length 8p(s) over R = F-pm + uF(pm) are completely determined for all unit lambda of the form lambda = xi(l) is an element of F-pm , where l is even. In addition, the algebraic structures of all cyclic and negacyclic codes of length 8p(s) over R are established in term of their generator polynomials. Dual codes of all cyclic and negacyclic codes of length 8p(s) over R are also investigated. Furthermore, we give the number of codewords in each of those cyclic and negacyclic codes. We also obtain the number of cyclic and negacyclic codes of length 8p(s) over R.
引用
收藏
页码：525 / 570
页数：46
相关论文
共 51 条
[1]   On the generators of Z4 cyclic codes of length 2e [J].
Abualrub, T ;
Oehmke, R .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (09) :2126-2133
[2]  
Al-Ashker MM, 2005, ARAB J SCI ENG, V30, P277
[3]  
[Anonymous], 1974, Pure Appl. Math.
[4]   Type II codes over F2+uF2 and applications to Hermitian modular forms [J].
Bannai, E ;
Harada, M ;
Ibukiyama, T ;
Munemasa, A ;
Oura, M .
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2003, 73 :13-42
[5]  
Berlekamp E.R., 1984, McGraw-Hill Series in Systems Science
[6]  
Berlekamp E.R., 1968, P C COMB MATH ITS AP, P298
[7]  
Berman S. D., 1967, Cybernetics, V3, P17, DOI 10.1007/BF01119999
[8]   Cyclic codes over Z4 of oddly even length [J].
Blackford, T .
DISCRETE APPLIED MATHEMATICS, 2003, 128 (01) :27-46
[9]   Negacyclic codes over Z4 of even length [J].
Blackford, T .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (06) :1417-1424
[10]   EXPLICIT FACTORIZATION OF X2K+1 OVER F(P) WITH PRIME P-EQUIVALENT-TO-3 MOD 4 [J].
BLAKE, IF ;
GAO, SH ;
MULLIN, RC .
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 1993, 4 (02) :89-94
123456