Genus-g Hyperelliptic Jacobian Weil Coefficient Parity Obstructions

This dataset contains conditions which disprove the existence of a hyperelliptic Jacobian in an isogeny class of abelian varieties over a finite field of characteristic 2. For each genus g from 5 to 20, there is an associated .txt file whose entries are elements of (Z/2Z)^g. Given a degree 2g q-Weil polynomial f(x), where q = 2^n, with Weil coefficients a_1,...,a_g, if (a_1,...,a_g) = (n_1,...,n_g) (mod 2) for any entry (n_1,...,n_g) in the genus_{g}.txt file, then f(x) is not the Frobenius polynomial of a genus-g hyperelliptic Jacobian.