Quantum / CONCEPT

The q = 2 Singer-quadric qubit codes have minimum distance 2 for every d >= 2

Kulhandjian and Hanzo (arXiv:2610.02392) build qubit stabilizer codes Q(2,d) from a Singer difference set and the quadric Tr(z^3) = 0 in PG(d,2), prove numerically for d <= 6 that the cross-correlation u = M_Q tau_H is the all-ones vector, and conjecture (Conjecture 24) that this and the resulting minimum distance 2 hold for every d >= 2. For every d >= 2 and every primitive element of GF(2^(d+1)), u is all-ones, every Z_i Z_j with i != j lies in the centralizer and not in the stabilizer row space, and no element of the centralizer outside the stabilizers has weight below 2.