On interleaved sequences over finite fields

Abstract

An (f(x),m)-interleaved sequence Gong (IEE Trans. Inform. Theory 41(2) (1995) 400) over a finite field F q is a sequence where all its m-decimated sequences have f(x) as the common characteristic polynomial, which can be determined by a control parameter. This paper demonstrates how issues such as minimal polynomial, linear span, period and correlation values of an (f(x),m)-interleaved sequence are related to its control parameter when f(x) is irreducible. Moreover, this paper shows how control parameters can be chosen to construct some sequences of maximal period and have optimal auto and cross correlation values among all the (f(x),m)-interleaved sequences when f(x) is primitive and m is less than the period of f(x).