Constacyclic Code And Its Gray Map Over Finite Chain Ring F_p^m+uF_p^m

Since the 90s of last century,the study of codes over finite rings has been widely concerned by scholars,there are some good results about coding over the special finite ring Fpm +uFpm.At the begining of twenty-first century,some researchers have studied the structure of(1-u)-constacyclic codes and cyclic codes over Fpm + uFpm by defining the Gray map with respect to homogeneous weight from Fpm＋uFpm to Fpmpm,where u2=0.In this paper,we consider Fpm as the m-dimensional vector space over Fp,for a given basis from Fpm to Fp,we define the Gray map with respect to Lee weight from Fpm + uFpm to Fp2m,then we study the structure of(a +bu)-constacyclic codes and cyclic codes over Fpm+uFpm,where u2 = 0,a≠ 0.For n≡p-1(mod p),we first prove that the Gray image of a(a + bu)-constacyclic code of length n over Fpm+uFpm is a distance-invariant(a,b)-minor quasi-cyclic code of index m and length 2mn over Fp.Furthermore,we show the condition for dual containing of constacyclic codes and a construction method of self-dual cyclic codes over Fpm + uFpm.Finally,for any b∈ Fpm,a=1,we prove that every code of length 2mn which is the Gray image of cyclic codes over Fpm+uFpm of length n is(a,b)-linear equivalent to a p-ary(a,b)-minor quasi-cyclic code of index m,where n≡ p-1(mod p).