  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.
