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A single deletion error correcting code (SDECC) is a set of fixed-lengthsequences consisting of two types of symbols, 0 and 1, such that the originalsequence can be recovered for at most one deletion error. The upper bound forthe 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 lengthis ten or less. In this paper, we discuss a method for calculating this upperbound by providing an integer linear programming solver with several linearconstraints. As a new result, we obtained that the tight upper bound for thesize of a single deletion error correcting code in dimension 11 is 172.

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