Constructions and bounds for codes with restricted overlaps

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

doi:10.1109/TIT.2023.3304712

Constructions and bounds for codes with restricted overlaps

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

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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.

Original language	English
Number of pages	17
Journal	IEEE Transactions on Information Theory
DOIs	https://doi.org/10.1109/TIT.2023.3304712
Publication status	Published - 14 Aug 2023

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10.1109/TIT.2023.3304712

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Cite this

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title = "Constructions and bounds for codes with restricted overlaps",

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.",

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AB - 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.

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