(1+λu)-Constacyclic codes over Fp[u]/〈um〉

Motivated by the work in [1] of Abualrub and Siap (2009), we investigate ( 1 + λ u ) -constacyclic codes over F p [ u ] / 〈 u m 〉 of an arbitrary length, where λ is a nonzero element of Fp. We find the generator polynomials of ( 1 + λ u ) -constacyclic codes over F p [ u ] / 〈 u m 〉 , and determine the number of ( 1 + λ u ) -constacyclic codes over 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 + λ u ) -constacyclic codes over Fp+uFp under a Gray map.