Factorizations Of Polynomials And Weight Distributions Of Reducible Cyclic Codes

Let Fq be a finite field.This paper mainly investigates an irreducible factorization of the polynomial xn-1 over Fq and weight distribution of cyclic codes of length n over Fq.In Chapter 1,we introduce the research background of this thesis and finally summarizes main results of this thesis.In Chapter 2,we introduce some basic concepts and preliminaries in detail.In Chapter 3,we investigate an irreducible factorization of the polynomial xn-lover Fq.In special,if ordrad(n)(q)=4,we give its irreducible factorization and count the number of its irreducible factors.In Chapter 4,we consider weight distribution of a cyclic code with two zeroes over Fq.In special,if rad(n)|(q-1)and q?7(mod 8),we obtain the weight distribution of a new cyclic code with two zero.This result generalizes the results of Zhu et al.in 2015.