  In this paper, we use a linear programming (LP) optimization approach to
evaluate the equivocation for a wiretap channel where the main channel is
noiseless, and the wiretap channel is a binary symmetric channel (BSC). Using
this technique, we present an analytical limit for the achievable secrecy rate
in the finite blocklength regime that is tighter than traditional fundamental
limits. We also propose a secrecy coding technique that outperforms random
binning codes. When there is one overhead bit, this coding technique is optimum
and achieves the analytical limit. For cases with additional bits of overhead,
our coding scheme can achieve equivocation rates close to the new limit.
Furthermore, we evaluate the patterns of the generator matrix and the
parity-check matrix for linear codes and we present binning techniques for both
linear and non-linear codes using two different approaches: recursive and
non-recursive. To our knowledge, this is the first optimization solution for
secrecy coding obtained through linear programming.
