Mathematical Analysis and Explicit Construction of a Rectangular CSS Surface Code with Parameters [[1024, 16, 8]]

Abstract

We present a rigorous, self-contained construction and full mathematical analysis of a CSS surface code on a 64x16 qubit lattice, encoding k=16 logical qubits in n=1024 physical qubits at distance d=8. The paper gives explicit algebraic definitions of the stabilizer generators, geometric proofs of the code parameters, GF(2) rank calculations establishing the code dimension, and executable Python code reproducing the construction and the rank computations. Note: the deposit files are under restricted access; the proofs and the code have not been independently verified from this record.