Basic Properties And Application Of Repeated-root Cyclic Codes

Cyclic codes, i.e., of linear block codes whose set of codewords is closed under cyclic shifting,enjoys a prominent place in the theory of error-correcting codes.In the theory of cyclic codes, it is common practice to require that (n,p) = 1, where n is the word length and F_q is the alphabet, p is the characteristic of F_q .This ensures that the generator g(x) of the cyclic code has no multiple zeros ( repeated roots) .we call those cyclic codes-(simple root cyclic codes). In this paper,we will discuss the case when the generator g(x) of the cyclic code has multiple zeros,i.e.,(n,p)≠1. we call those cyclic codes Repeated-Root Cyclic codes.The periodic sequence has good application in the theory of stream cipher, and also has good Properties.nowadays ,conclusions of periodic sequence are very ripe. periodic sequence is closely related to Repeated-Root Cyclic codes. but,nowadays there are so little results between periodic sequence and Repeated-Root Cyclic codes. Then in this paper we will discuss the relation ship with each other.and conside the interaction of each other.In this article, we will most probably discuss the expresses between periodic sequence and Repeated-Root Cyclic codes,the availability of each other,the relationship of spectral analysis between each other, we also discuss the contact of distance of Repeated-Root Cyclic codes and k-error linear complexity of periodic sequence.and this work will have the improvement and impetus function to theoretical results of Cryptography.