Quasi-cyclic Subcodes Of A Class Of Cyclic Codes

Being an important class of linear codes,cyclic codes have been widely concerned since they were proposed because of the simplicity of their coding and decoding algorithms.Quasi-cyclic codes which are extended from cyclic codes have also become a research focus.In this dissertation,we mainly study the quasi-cyclic subcodes of the cyclic code C,which is the dual of the binary double-error-correcting BCH code of length N=2n-1.We list all possible indices of the quasi-cyclic subcodes,and determine the number of quasi-cyclic subcodes corresponding to a certain index.The details are as follows:Firstly,for an arbitrarily length n,we give the general representation of the indices of the quasi-cyclic subcodes and the number of quasi-cyclic subcodes corresponding to a certain index.These results are based on the trace representation of C.Secondly,in three cases(I:2(?)n;?:2|n but 3(?)n;?:2|n and 3|n),we concretely calculate the indices of the quasi-cyclic subcodes and the number of quasi-cyclic subcodes corresponding to a certain index.