Research On A Class Of Repeated-root Constacyclic Codes Over Finite Field

Constacyclic codes are linear codes with good algebraic structure,they are useful for efficient coding by simple shift register.In addition,constacyclic codes have efficient decoding algorithms.Constacyclic codes not only have important theoretical significance,but also have practical application value.Let F_q be a finite field with character p and p?3 l?3 be different odd primes.And let F_q*=<?>be the multiplicative cyclic group consisted of non-zero elements over F_q,where ? is a primitive(q-1)th root of unity.In this paper,we study constacyclic codes of length 6lps over finite field F_q.We mainly study the following contents:(1)Using n-equivalent,it can be known that the number of nonequivalent repeated-root codes classes are d=gcd(6lps,q-1).By the theory of q-cyclotomic cosets and so on,the generator polynomials of all constacyclic codes and their duals are given over F_q.And then,consider the case where 1 is equal to 1,the minimum Hamming distances of all cyclic codes of length 6ps over F_q are given.(2)According to the structure of these repeated-root constacyclic codes,the characterization and enumeration of linear complementary dual(LCD)and self-dual constacyclic codes of length 6lps are obtained over F_q.