Research On The Distance Distributions Of Codes Over F_p^m+uF_p^m+…+u^k-1F_p^m

In this paper, we mainly study the distance distribution of several classes of constacyclic codes over the polynomial ring Fpm+uFpm+…+uk-1Fpm,and the bounds on the minimum homogeneous distance of pk-ary image of linear block codes over such polynomial rings.The details are given as follows:(1)We study the homogeneous distance distribution of(1+u)-constacyclic codes over the ring Fpm+uFpm+…+uk-1Fpm of arbitrary lengths.Firstly,the torsion code of a(1+u)-constacyclic code over Fpm+uFpm…+uk-1Fpm for a given length are introduced.Then,by using the torsion codes,a bound for the homogeneous distance of (1+u)-constacyclic codes over the ring of any length is given. The exact homogeneous distance of some (1+u)-constacyclic codes over Fpm+uFpm+…+uk-1Fpm is also obtained.(2) We study the Hamming distance and homogeneous distance of (uλ-1)-constacyclic codes of lenth2ps over the ring Fpm+uFpm+…+uk-1Fpm. p is divided into two cases:p三3(mod4)and p三1(mod4).The distance distribution of each case is given.(3)We study the bounds on the minimum homogeneous distance of pk-ary image of linear block codes over the ring Fpm+uFpm+…+uk-1Fpm.Based on the linear block codes over the ring Pm=Fpm+uFpm+…+uk-1Fpm,definition of homogeneous weigth over P1=Fp+uFp+…+uk-1Fp,and the Plotkin bounds over Frobenius ring,by using the map μ:Pm→P1,the bounds on the minimum homogeneous distance of pk-ary image of linear block codes over the ring pm...