Codes over finite fields for multidimensional signals

In this paper, linear block codes over finite fields of the algebraic integer ring of the cyclotomic field Q(e(2 pii/n)) module irreducible elements are presented, where n epsilon {3, 4, 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}. These codes can be used for coding over phi>(*) over bar * (n) dimensional signal space and can correct one error taken from the group of all roots of unity in the algebraic integer ring of Q(e(2 pii/n)). These codes provide an algebraic approach in an area which is currently mainly dominated by nonalgebraic convolutional codes. (C) 2000 Academic Press.