Research On Two Classes Of Repeated-root Constacyclic Codes

In this paper,we mainly study two classes of repeated-root constacyclic codes.The details are given as follows:(1)Let p? 3 be any prime and l?3 be any odd prime with gcd(p,l)= 1.The multiplicative group Fq*=<?>can be decomposed into mutually disjoint union ofgcd(q-1,3lps)cosets over the subgroup(?3lps),where ? is a primitive(q-1)th root of unity,q= pm with m is a positive integer.We classify all repeated-root constacyclic codes of length 3lps over the finite field Fq into some equivalence classes by this decomposition.According to these equivalence classes,we explicitly determine the generator polynomials of all repeated-root constacyclic codes of length 3lps over Fq and their dual codes.Self-dual cyclic codes of length 3lps overFq exist only when p = 2.We give all self-dual cyclic codes of length 3·2s l over F2m and their enumeration.We also determine the minimum Hamming distance of these codes when gcd(3,q-1)=1 and l = 1.(2)Let R = Z4 + uZ4,Rn= R[x]/(xn-(2u-1)),whereu2 =0,n = 2e.By studying the structures of(2u-1)-constacyclic codes of length n over R,we obtain the generators for these codes and classify all(2u-1)-constacyclic codes of length n over R.Furthermore,we study the minimum Hamming distance of(2u-1)-constacyclic codes of length n over R.We also give the structures of the duals of(2u-1)-constacyclic codes of length n over R.Finally,we list all self-orthogonal and self-dual(2u-1)-constacyclic codes of length n over R.