Notes on q - ary Interleaved Sequences ?

A sequence u over a nite eld Fq is called an (f(x); m)-interleaved sequence 1] if f(x) is a common characteristic polynomial of all its m-decimated sequences. This paper demonstrate how the subjects such as the minimal polynomial, the linear span, the period and the correlation values of an (f(x); m)-interleaved sequence are related to its m-decimated sequences when f(x) is irreducible, and makes a correction to an error made in 1] in studying the same problem. Moreover, this paper shows how to choose the m-decimated sequences to construct some sequences with the optimal auto and cross correlation values among the (f(x);m)-interleaved sequences when f(x) is primitive and m is less than the period of f(x).