Reinforcement learning decoding for Hermitian AG quantum stabilizer codes

Abstract We provide a corrected, consistent development of classical algebraic geometry (AG) codes and associated nonbinary quantum stabilizer codes built fromthe Hermitian curve yq+y=xq+1 over . This resolves earlier inconsistencies around the choice of m, point counts, dual indices, and field of the inner product. The curve has genus g=q(q-1)/2, q³+1 -rational points, and a unique point at infinity; setting D to be the sum of all affine -points gives length n= D=q³. For one-point divisors G=rP_∞ we give a monomial basis for L(G), the standard duality formula CL(D,rP_∞)^⊥=CL\!(D,(n+2g-2-r)P_∞), and a simple sufficient condition for Hermitian self-orthogonality: (q+1)r≤ n+2g-2 (equivalently, r≤ q²-2).Under this condition, Ashikhmin--Knill yields q-ary stabilizer codes [[n,n-2k,≥ dH^⊥]]q with k= CL(D,rP_∞) and dH^⊥≥ r-2g+2.We also retain a complete reinforcement-learning (RL) section: an RL-on-Greedy decoder that first applies a greedy pass then a Deep Q-Network to resolve residual syndromes. We include the original evaluation plot and all references, and clarify that the RL case study can be applied to any stabilizer code (including, but not limited to, those from Hermitian AG codes).