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Computer Science > Information Theory

arXiv:2309.14736 (cs)
[Submitted on 26 Sep 2023]

Title:The Tight Upper Bound for the Size of Single Deletion Error Correcting Codes in Dimension 11

Authors:Kazuhisa Nakasho, Manabu Hagiwara, Austin Anderson, J. B. Nation
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Abstract:A single deletion error correcting code (SDECC) is a set of fixed-length sequences consisting of two types of symbols, 0 and 1, such that the original sequence can be recovered for at most one deletion error. The upper bound for the size of SDECC is expected to be equal to the size of Varshamov-Tenengolts (VT) code, and this conjecture had been shown to be true when the code length is ten or less. In this paper, we discuss a method for calculating this upper bound by providing an integer linear programming solver with several linear constraints. As a new result, we obtained that the tight upper bound for the size of a single deletion error correcting code in dimension 11 is 172.
Subjects: Information Theory (cs.IT)
MSC classes: 68P30
ACM classes: E.4; G.2.1
Cite as: arXiv:2309.14736 [cs.IT]
  (or arXiv:2309.14736v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2309.14736

Submission history

From: Kazuhisa Nakasho [view email]
[v1] Tue, 26 Sep 2023 08:00:08 UTC (19 KB)
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