Level 163 stabilizer extraction from Hecke syndrome geometry

From Q=ker(T2^2), the projective points P(Q) form 13 points and the parity matrix H in M(3x13)(F_3) has H H^T=0, yielding the ternary Hamming code C=ker(H) with [13,10,3].

• dim C = 10
• dim C^perp = 3
• C^perp subseteq C: True
• d(C)= 3, d(C^perp)= 9
• d(C/C^perp)= 3
• CSS distance = min(d(C^perp),d(C/Cperp))=3
• Stabilizer code parameters: [[13,7,3]]_3

Hecke action on Q (mod 3) and projective point coordinates: - Invertible generators checked: 7, 43, 67, 163 - Non-invertible generators (det=0): 3, 11, 19 - For each invertible generator p, there is a monomial matrix S_p = diag(scales_p)·P_p on the 13 coordinates of C such that H·S_p has the same row space as H. - Hence each generator preserves both C and C^, and the Hecke-induced group acts by code automorphisms of the CSS pair (C,C^).