The Weight Distribution Of A Class Of Constacyclic Codes

The weight distribution of cyclic codes is a central subject of the coding theory, but it is a very difficult problem to obtain the weight distribution of the general cyclic codes. There are a few more abundant research results can be used to calculate the weight distribution of some special constacyclic code, including gaussian and gaussian cycle, pseudo-random sequence method and so on.In this paper, we will study the weight distribution of a special constacyclic codes, and bying the decompositon of the base set of the generator polynomial to calculate the weight distribution of this class of constacyclic codes. Let Fq be a finite field with q elements. For a non zero element λ in Fq, we consider λ-onstacyclic codes of length N over Fq, where the characteristic of Fq does not divide N. We give the sufficient conditions when a λ- constacylic codes of length N over Fq has generator polynomial of the form x2n+bxn+b2, where 0≠b∈Fq. Then we will divide the bases of the λ- constacylic code which is generated by the polynomial of the form x2n+bxn+b2 into groups, and get the weight distribution of the λ- constacylic code by calculating the weight distribution of the code Cs which is generated by the base group.