The Constructions Of Constacyclic Codes Over The Finite Field F_q

Cyclic codes are a kind of linear error correcting codes and very important since they have the most striking features as follows:(1)They can be easily encoded by feedback linear shift registers;(2)Various simple and practical decoding methods can be found.As a generalization of cyclic codes,constacyclic codes can also be effectively encoded through shift registers.They play an important role as well in error correction code theory and are the preferred objects in engineering applications.So far,the properties and the structures of a large number of A constacyclic codes with different lengths have been described which makes great progress in the research of A constacyclic codes.However,the lengths of the constructed A constacyclic codes n are still narrow,the lengths of the given A constacyclic codes do not exceed three prime factors in the factorization.This is still far from the general case of n.Based on previous work,this thesis extends the lengths of A constacyclic codes,the lengths contain at least four prime factors;the generator polynomials of these ? constacyclic codes are given;the corresponding A constacyclic codes are then constructed.Firstly,in the finite field IFq with q=pn elements(where p is the characteristic of Fq and k,l,m,p are different odd prime numbers),the cyclotomic cosets of q module klm and qk module lm are given.Secondly,by using the relation between cyclotomic cosets and irreducible polynomial,the generator polynomials of A constacyclic codes with lengths klmpn and length 2klmpn are obtained.Finally,A constacyclic codes with lengths klmpn and lengths 2klmpn are constructed.