<i>Q</i>-Ary (<i>t</i><sub>1</sub>, <i>t</i><sub>2</sub>)-Overlap-Free Codes

A (t1, t2)-overlap-free code is a set of sequences such that for all integers i with t1 ≤ i ≤ t2, no prefix of length i of any sequence is the suffix of any sequence (not necessarily distinct) in the set. In this paper, we first present a generalized construction of (t1, t2)-overlap-free codes and analyze the size of the code via generating functions. We then investigate the non-expandable property of (1, t)-overlap-free codes. Finally, we give the size of the (1, t)-overlap-free codes under certain constraint conditions.