Notes on q-ary interleaved sequences

(f(x), m)-interleaved sequences over Fq have been proposed and studied. Roughly speaking, an (f(x), m)-interleaved sequence is a sequence which is made of (or say, interleaved by)m component sequences with a common characteristic polynomial (f(x)(∈ Fqx]). In this note, (f(x), m)-interleaved sequences are studied further. As a result, it is made clear how their minimal characteristic polynomials, linear spans and periods are determined by their component sequences. And also, their period distribution and the number of (f(x), m)-interleaved sequences with maximal linear spans are derived. Furthermore, a large number of interleaved sequences with the lowest correlation among all the (f(x), m)-interleaved sequences are constructed.