Research On Constacyclic Codes Of Length Composite Number Over Finite Fields

One of the main problems of coding theory is the construction of codes with good parameter through variety of ways.In recent years,many works devote to study special type of constacyclic codes of length composite number over finite fields.Researchers mainly research the structure and properties of these codes,which provide more theoretical basis of constructing good codes.Firstly,in chapter 3,we mainly research minimal cyclic codes of length pnqm over Fl.We give a simple and direct method to obtain expressions for all the mnd+m +n 1 l-cyclotomic cosets.Furthermore,primitive idempotents are obtained.The generator polynomial,dimension and minimum Hamming distance of the minimal cyclic code of length pnqm in Fl[x]/(xpnqm-1>are also discussed.As an example,we give all the minimal cyclic codes of length 175 over F3;Secondly,in chapter 4,we discuss cyclic codes of length pnq2 over Fl.We give all the cyclic codes of length pnq2 over Fl.From this,we explicitly determine expressions and enumeration formulas of all the self-orthogonal cyclic codes and LCD cyclic codes of length pnq2 over Fl,respectively.As an example,we give all the expressions and enumeration formulas of all the self-orthogonal cyclic codes and LCD codes of length 175 over F3;Finally,in chapter 5,we study self-orthogonal and self-dual repeated root negacyclic codes of length 2n ps over Fq.We obtain expression and enumeration formulas of all the self-orthogonal and self-dual repeated-root negacyclic codes of length 2nps over Fq.As an example,the generator polynomialand and parameter of all the self-dual repeated-root negacyclic codes of length 10 over F5 are discussed and some better codes are derived.