  A new method is explored for analyzing the performance of coset codes over
the binary erasure wiretap channel (BEWC) by decomposing the code over
subspaces of the code space. This technique leads to an improved algorithm for
calculating equivocation loss. It also provides a continuous-valued function
for equivocation loss, permitting proofs of local optimality for certain
finite-blocklength code constructions, including a code formed by excluding
from the generator matrix all columns which lie within a particular subspace.
Subspace decomposition is also used to explore the properties of an alternative
secrecy code metric, the chi squared divergence. The chi squared divergence is
shown to be far simpler to calculate than equivocation loss. Additionally, the
codes which are shown to be locally optimal in terms of equivocation are also
proved to be globally optimal in terms of chi squared divergence.
