Research And Application Of Some Classes Of Repeated-Root Constacyclic Codes Over Finite Fields

Cyclic codes are a kind of important linear codes.Due to the important theoretical and practical values,scholars begin to pay attention to the constacyclic codes which are more general than cyclic codes.They are natural extension of cyclic codes and can be realized by shift registers in technology.Let p is the characterization of Fq,q=pm,k,p,and l are different odd primes.In this thesis,we study constacyclic codes of length 2klmpn over finite field Fq.On the one hand,structure of constacyclic codes of length 2klmpn over the finite field Fq of characteristic p and their duals are established in terms of their generator polynomials.The characterization and enumeration of all self-dual constacyclic codes of length 2klmpn are obtained.On the other hand,the dual inclusion of the repeated-root cyclic codes of length 4ps over Fq used.Based on algebraic q are structure of the repeated-root cyclic codes,combine with a necessary and sufficient condition for the repeated-root cyclic of length 4ps over Fq which contain their dual codes,and their minimum distance is determined.Based on Steane entanglement construction,several kinds of non binary quantum codes with better parameters are constructed.