(1+?u)-Constacyclic codes over Fp[u]/?um? ?
Motivated by the work in [1] of Abualrub and Siap (2009), we investigate (1+?u) ( 1 + ? u ) -constacyclic codes over Fp[u]/?um? F p [ u ] / ? u m ? of an arbitrary length, where ? ? is a nonzero element of Fp. We find the generator polynomials of (1+?u) ( 1 + ? u ) -constacyclic codes over Fp[u]/?um? F p [ u ] / ? u m ? , and determine the number of (1+?u) ( 1 + ? u ) -constacyclic codes over Fp[u]/?um? F p [ u ] / ? u m ? for a given length, as well as the number of codewords in each such code. Some optimal linear codes over F3 and F5 are constructed from (1+?u) ( 1 + ? u ) -constacyclic codes over Fp+uFp under a Gray map.
generator polynomial linear codes gray map constacyclic codes