Linear Block Codes for Four-Dimensional Signals

In this paper, linear block codes over finite fields of the algebraic integer ring of the cyclotomic fieldQ(e2πi/n) modulo irreducible elements are presented, wheren=5, 8, or 12. These codes can be used for coding over four-dimensional signal space and can correct one error which takes from the group of all roots of unity in the algebraic integer ring ofQ(e2πi/n), wheren=5, 8, or 12.