Period Distribution Of Linear Codes

Nguyen and Massey discovered those codewords which period reaches maximal value could be used to construct discrete signals having optimal generalized Hamming correlated characteristic in frequency-hopping system andmulti-address collision channel in 1988, so he put forward problem about number of the codewords without inner period and gave lower boundr0≥(q-1)qk-1.but he didn't gave exact value of T0.By using Fourier transform and Polya counting formula of GF(q) , Yang Yixian firstly solved the problem and got exact value of T0,and definitely presentedconcept of period distribution for error-correcting codes.Period distribution of linear code is one kind enumeration problem resemble weight distribution.It not only help to confirm design codes which havesequences with optimal Hamming correlation properties and tounderstand close interior structure of error-correcting codes, but also help to achieve distortionless compression of information , so it attracted much attention lately.In this paper we further study the properties of period distribution of linear codes on the fundamental results, a few new results are proved.It mostly includes thereinafter several aspects:1. By using the relation of period distribution of dual codes, the period distribution and general period distribution of binary BCH code which design distance is five are given.2. Some properties of general period for linear codes are studied and its algebraic structures are originally constructed.3. By using depth distribution, the period distribution of the Hamming codeand the extended Hamming code are determined.