Two 668-order m-modular Hadamard matrices for m = 128 and m = 500

This dataset contains two square {-1, +1} matrices of order 668 in CSV format. The file MH668_m128.csv satisfies H H^T ≡ 668 I (mod 128), and the file MH668_m500.csv satisfies H H^T ≡ 668 I (mod 500). Equivalently, for each matrix, all off-diagonal row inner products are congruent to 0 modulo the corresponding modulus m, while every diagonal entry of H H^T is exactly 668. Each CSV file has 668 rows and 668 columns, with no header row or index column. The dataset also includes a Python verification script, a requirements file, license information, and SHA-256 checksums for reproducibility. AI Use Disclosure: Generative AI made substantive contributions to the core construction presented in this work.