Nonlinear block codes for multidimensional signals

In this paper, one subgroup of the multiplicative group of units in the algebraicinteger ring of the cyclotomic field ℚ(e^2πi/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.