Journal Article

Nonlinear block codes for multidimensional signals

Xue-Dong Dong, Cheong Boon Soh and Erry Gunawan

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 17, issue 2, pages 191-207
Published in print June 2000 | ISSN: 0265-0754
Published online June 2000 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/17.2.191
Nonlinear block codes for multidimensional signals

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In this paper, one subgroup of the multiplicative group of units in the algebraicinteger ring of the cyclotomic field ℚ(e2πi/m) modulo the ideal (qn) has been decomposed into a direct product of cyclic groups, where m ∈ A = {5,7,8,9,11,12,13,15,16,17, 19, 20,21, 24, 25, 27, 28, 32, 33, 35, 36,40,44, 45, 48, 60, 84},q is a given prime integer, and n is a positive integer. The subgroup can be used to obtain a ϕ(m)-dimensional signal space and to construct block codes, over algebraic integers, which are able to correct some error patterns, where ϕ is the Euler function.

Keywords: algebraic-integer ring; block code; cyclotomic field; multidimensional signal space

Journal Article.  0 words. 

Subjects: Mathematics

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