The increasing threat posed by quantum computing to classical public-key cryptography has accelerated the development of Post-Quantum Cryptographic (PQC) schemes. Within this context, the National Institute of Standards and Technology (NIST) has run multiple standardization rounds for post-quantum schemes. One notable candidate from recent rounds is the Linear Equivalence Signature Scheme (LESS), a code-based signature construction whose security relies on the hardness of the Linear Code Equivalence problem. LESS derives signatures by applying the Fiat–Shamir transform to a zero-knowledge identification protocol, whose main computations manipulate large generator matrices over finite fields and apply monomial isometries. As a result, the scheme relies heavily on linear algebra operations, with the reduction of the generator matrix to the Reduced Row Echelon Form (RREF) representing a major bottleneck.