2025/06/03 by Vahid Nourozi, Nourozi, Vahid
Computer Science · #Coding theory and cryptography #FOS: Mathematics #FOS: Physical sciences #Quantum Algebra (math.QA) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2506.03397
openalex publication_date 2025/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct new classical Goppa codes and corresponding quantum stabilizer codes from plane curves defined by separated polynomials. In particular, over \mathbbF3 with the Hermitian curve y3 + y = x4, we obtain a ternary code of length 27, dimension 13, distance 4, which yields a [[27, 13, 4]]3 quantum code. To decode, we introduce an RL-on-Greedy algorithm: first apply a standard greedy syndrome decoder, then use a trained Deep Q-Network to correct any residual syndrome. Simulation under a depolarizing noise model shows that RL-on-Greedy dramatically reduces logical failure compared to greedy alone. Our work thus broadens the class of Goppa- and quantum-stabilizer codes from separated-polynomial curves and delivers a learned decoder with near-optimal performance.