The Higher Weight Enumerators of the Doubly-Even, Self-Dual $[48, 24, 12]$ Code

An efficient algorithm is presented for calculating higher weight enumerators of linear codes given generator matrices. By this algorithm, the higher weight enumerators of the unique doubly-even, self-dual code are calculated. The algorithm is based on a previously shown relationship between Tutte polynomials and higher weight enumerators.