Impact of symplectic structure on decoding complexity

Characterize how symplectic structure in symplectic linear-algebraic constraints influences the computational complexity of decoding problems, including whether and how it changes average-case hardness relative to classical linear decoding tasks such as LPN.

Background

SympLPN introduces symplectic orthogonality constraints absent in standard LPN. The constructions and reductions in the paper require new scrambling techniques tailored to symplectic subspaces, indicating deeper complexity-theoretic distinctions.

A systematic understanding of these effects would inform both hardness assumptions for post-quantum cryptography and algorithmic approaches to decoding quantum stabilizer codes.