English

Constructions and bounds for codes with restricted overlaps

Information Theory 2023-08-23 v4 Discrete Mathematics Combinatorics math.IT

Abstract

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden. We prove some general bounds and we give several constructions in the case of binary codes. Our techniques also allow us to provide an alternative, elementary proof of a lower bound on non-overlapping codes due to Levenshtein in 1964.

Keywords

Cite

@article{arxiv.2211.10309,
  title  = {Constructions and bounds for codes with restricted overlaps},
  author = {Simon R. Blackburn and Navid Nasr Esfahani and Donald L. Kreher and Douglas R. Stinson},
  journal= {arXiv preprint arXiv:2211.10309},
  year   = {2023}
}

Comments

17 pages. Theorems etc renumbered

R2 v1 2026-06-28T06:13:30.147Z