Constructions and bounds for codes with restricted overlaps

Simon Blackburn, Navid Esfahani, Donald Kreher, Douglas R. Stinson

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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.
Original languageEnglish
Number of pages17
JournalIEEE Transactions on Information Theory
Publication statusPublished - 14 Aug 2023

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