  We introduce two notions of discrepancy between binary vectors, which are not
metric functions in general but nonetheless capture the mathematical structure
of the binary asymmetric channel. In turn, these lead to two new fundamental
parameters of binary error-correcting codes, both of which measure the
probability that the maximum likelihood decoder fails. We then derive various
bounds for the cardinality and weight distribution of a binary code in terms of
these new parameters, giving examples of codes meeting the bounds with
equality.
