On harmonic weight enumerators of binary codes
We define some new polynomials associated to a linear binary code and a harmonic function of degree k. The case k=0 is the usual weight enumerator of the code. When divided by (xy)(k), they satisfy a MacWilliams type equality. When applied to certain harmonic functions constructed from Hahn polynomials, they can compute some information on the intersection numbers of the code. As an application, we classify the extremal even formally self-dual codes of length 12.
weight enumerator codes harmonic functions formally self-dual codes