Back to the Future
summary
History connects concrete claims: Reed–Muller families are proved to achieve capacity on the binary erasure channel by combining their full symmetry with sharp-threshold results; second-order RM weight distributions are derived by a number‑theorist square‑the‑sum trick showing weights divisible by powers of 2. On the quantum side, explicit CSS constructions use symplectic matrices and coset‑weight congruences (coset weights congruent mod 8) to produce codes fixed by diagonal gates and to climb the Clifford hierarchy; worked examples and papers appear (one in Quantum, one on archive).
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