Exact Minimum Distance of a [[832,10]] Quantum LDPC Code: d = 15 by Exact Fold and Lift Enumeration

We determine the exact minimum distance of a two block quasi cyclic CSS code with 832 physical and 10 logical qubits. Earlier work had shown 10 ≤ d ≤ 15. We close the interval and prove d = 15. In each CSS sector the classical kernel has no nonzero word of weight 1 to 14 and exactly 416 words of weight 15, one orbit under cyclic shifts, all of them nontrivial logical operators. The proof uses the identity x^(2m) + 1 = (x^m + 1)^2 over GF(2). Since 416 = 13 · 2^5, the kernel folds down to a 26 bit code and lifts back exactly, so all low weight words can be enumerated level by level in about one second per sector. The paper gives the full proofs, the results, an 18 check validation suite, and the limits: this is a computer assisted proof, not a formally verified one. The code matrices and source files are not part of this record. They are held in a separate restricted record [restricted record link], and SHA256 digests in the paper pin every file.