A linear code is a subspace of a finite-dimensional vector space defined over a finite field; a code is self-dual if it is its own orthogonal complement. The simplest such code is {00, 11}. These codes are of theoretical interest because of their connections with classical invariant theory.

This paper illustrates the difference between theory and computation: Pless determined the number of binary (that is, defined over the field with two elements) self-dual codes in the 1970s, but there has evidently been no effort, until recently, to compute all of these codes. This paper offers the first enumeration of all such codes in the non-trivial case of length 32. Nearly half of the paper consists of tables that include the full weight spectrum of each code and, for counting purposes, the size of its automorphism group.

The algorithms used are specific to the case of binary codes, and seem to be of the type that is difficult to generalize to codes over larger fields.

There is an interesting by-product of the calculation: the literature is full of partial results on such codes, and with the exception of one typographical error, this computation agrees with all of them. Whether this vindicates theory or computation probably depends on one’s personal perspective.