On some special codes over Fp+uFp+u2Fp

Abstract

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