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(e2πi/n) modulo irreducible elements are presented, where n {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 (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(e2πi/n). These codes provide an algebraic approach in an area which is currently mainly dominated by nonalgebraic convolutional codes.