Cocyclic Butson Hadamard matrices and codes over Zn via the trace map

被引：0

作者：

Pinnawala, N. ^{[1
]}

Rao, A. ^{[1
]}

机构：

[1] Royal Melbourne Inst Technol, Sch Math & Geospatial Sci, Melbourne, Vic 3001, Australia

来源：

FINITE FIELDS AND APPLICATIONS | 2008年 / 461卷

关键词：

cocycle; complex Hadamard; Butson; simplex codes; trace; exponent;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Over the past couple of years trace maps over Galois fields and Galois rings have been used very successfully to construct cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and subsequently to generate simplex codes over Z(4), Z(2)s and Z(p) and new linear codes over Z(p)s. Here we define a new map, the trace-like map and more generally the weighted-trace map and extend these techniques to construct cocyclic Butson Hadamard matrices of order n(m) for all n and m and linear and non-linear codes over Z(n).

引用

页码：213 / 228

页数：16

共 14 条

[1]

Baliga A., 1998, Journal of Combinatorial Mathematics and Combinatorial Computing, V28, P7

[2]

Baliga A., 1995, AUSTRALAS J COMB, V11, P123

[3] Transform approach to permutation groups of cyclic codes over Galois rings [J].

Blackford, Jason Thomas ;

Ray-Chaudhuri, Dwijendra K. .

2000, IEEE, Piscataway, NJ, United States (46)

[4]

Butson A. T., 1962, Proc. Am. Math. Soc, V13, P894, DOI [https://doi.org/10.2307/2034082, DOI 10.2307/2034082, 10.1090/S0002-9939-1962-0142557-0]

[5]

Calderbank A. R., 1995, Designs, Codes and Cryptography, V6, P21, DOI 10.1007/BF01390768

[6]

DRAKE DA, 1979, CAN J MATH, V31, P217

[7]

GARETH AJ, 1998, ELEMENTARY NUMBER TH

[8]

GUPTA MK, 2001, LNCS, V2227, P112

[9] Fourier transforms from a weighted trace map [J].

Horadam, K. J. ;

Rao, A. .

2006 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1-6, PROCEEDINGS, 2006, :1080-+

[10]

Lidl R., 1997, FINITE FIELDS

← 1 2 →