On some special codes over Fp + uFp + u2Fp

摘要

We define a new map between codes over Fp + uFp + u2Fp and Fp which is different to that defined in [2]. It is proved that the image of the linear cyclic code over the commutative ring Fp + uFp + u2Fp with length n under this map is a distance-invariant quasi-cyclic code of index p2 with length p2n over Fp. Moreover, it is proved that, if (n, p) = 1, then every code with length p2n over Fp which is the image of a linear (1 − u2)-cyclic code with length n over Fp + uFp + u2Fp under this map is permutation equivalent to a quasi-cyclic code of index p2.