Relation between weight distribution and combinatorial identities (Q2706955)

The MacWilliams equations and Pless power moment [\textit{V. Pless}, Introduction to the theory of error-correcting codes (3rd ed., Wiley Interscience Series in Discrete Mathematics and Optimization, John Wiley \& Sons) (1998; Zbl 0928.94008)] give combinatorial relations between the weight distributions of a binary linear code and of its dual code. Instead of the usual application of these identities to find the weight distribution of a dual code, the author applies the identities to codes for which both the code and its dual have known simple weight distributions. Trivial codes give new proofs of well-known identities, while other codes give new identities.