Properties of Interleaved Sequences Created from M-Sequences

Maximal-length sequences or m-sequences over a finite field F(q) are a well-known and studied class of sequences with desirable properties such as balance of both individual elements and tuples. Interleaved sequences are created by combining a base sequence of period s and a shift sequence e of length T, consisting of elements from Z(q) plus an element of infinity. This thesis examines interleaved sequences to determine which properties of m-sequences are preserved when the m-sequence is used as a base sequence. First an equivalence relation on shift sequences is defined, with two operations that can be applied to these sequences. Palindromic sequences are defined, and the exact conditions for the interleaved sequence to also be palindromic are given. We prove that the length of the interleaved sequence is ST/n when n|T and gcd(n,s)=1. The results of experimentation on using the interleaved sequences to construct covering arrays are given.