The Distribution of Homogeneous Distance of (1+u)-constacyclic Codes over Fpm+uFpm++uk-1Fpm

In this paper, the distribution of homogeneous distance of (1+u)-constacyclic codes over the ring Rk=Fpm+uFpm++uk-1Fpmof arbitrary lengths is studied. Firstly, the torsion codes of a (1+u)-constacyclic code overRk for a given length are introduced. Then, by using the torsion codes, a bound for the homogeneous distance of (1+u)-constacyclic codes overRk of any length is given. The exact homogeneous distance of some (1+u)-constacyclic codes over Rk is also obtained.