  Coding theory is very useful for real world applications. A notable example
is digital television. Basically, coding theory is to study a way of detecting
and/or correcting data that may be true or false. Moreover coding theory is an
area of mathematics, in which there is an interplay between many branches of
mathematics, e.g., abstract algebra, combinatorics, discrete geometry,
information theory, etc. In this paper we propose a novel approach for
analyzing proof nets of Multiplicative Linear Logic (MLL) by coding theory. We
define families of proof structures and introduce a metric space for each
family. In each family, 1. an MLL proof net is a true code element; 2. a proof
structure that is not an MLL proof net is a false (or corrupted) code element.
The definition of our metrics reflects the duality of the multiplicative
connectives elegantly. In this paper we show that in the framework one
error-detecting is possible but one error-correcting not. Our proof of the
impossibility of one error-correcting is interesting in the sense that a proof
theoretical property is proved using a graph theoretical argument. In addition,
we show that affine logic and MLL + MIX are not appropriate for this framework.
That explains why MLL is better than such similar logics.
