Algebraic structure of cyclic codes over M3(Fp)

Abstract

Let Fp  be the finite field of order p and M3(Fp)  the ring of 3 × 3  matrices over Fp,  where p  is a prime. For certain prime p, we determine the complete algebraic properties of cyclic codes of length N (p | N) over M3(Fp).  We define an isometry from M3(Fp)  to Fp3 + eFp3 + e2Fp3,  where  e3 = 1. As an outcome, we derive numerous optimal and good linear F8  codes induced from F8 -images of cyclic codes over M3(F2).