Quantum LDPC Codes from Polynomial Minors

Abstract:We construct quantum codes from codewords of a cyclic code and the minors of a polynomial matrix. The construction uses a two-row, three-column matrix whose minors yield a second matrix satisfying the CSS orthogonality condition. We derive the code dimension from the greatest common divisors of the entries and minors, with a simplified formula for odd lifting factors. A residue characterization identifies additional common factors of the minors and leads to a method for controlling the dimension through polynomial selection. We also give a condition for changing the minor generator without changing the code. Explicit polynomial constructions yield 13 quantum codes with verified minimum distances, including a $[[255,80,12]]$ code of rate $80/255$.

Quantum Physics (quant-ph); Quantum Algebra (math.QA)

arXiv:2610.19459 [quant-ph]

(or arXiv:2610.19459v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.19459 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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