The Depth Distribution Of Cyclic Codes

In 1997, T.Etzion introduced depth distribution of linear codes,and proved that the depth distribution of the nonzero codewords of an [n,k] linear code consists of exactly k nonzero values, and its generator matrix can be constructed from any k nonzero codewords with distinct depths;In 1998, C. J. Mitchell studied rational polynomial, gave depth spectrum of cyclic code. In 2000, Luo gave a general formula for computing the depth distribution of linear code,by using method of matrix and system of linear equations. We study the algorithms of depth distribution of linear codes,and the main results are as follows:We give a different proof of T.Etzion and C. J. Mitchell' main results from the linear property of difference;extend C J. Mitchell' conclusions,give depth spectrum of cyclic code over finite field.