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PreprintCC BY 4.0arXiv

Quantum LDPC Codes from Polynomial Minors

  • Vahid Nourozi
  • Roxana Smarandache
  • David G. M. Mitchell
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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.

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Cite

BibTeXRIS
BibTeX
@misc{nourozi2026quantum,
  title = {{Quantum LDPC Codes from Polynomial Minors}},
  author = {Vahid Nourozi and Roxana Smarandache and David G. M. Mitchell},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19459},
  eprint = {2610.19459},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19459},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantum LDPC Codes from Polynomial Minors
AU  - Vahid Nourozi
AU  - Roxana Smarandache
AU  - David G. M. Mitchell
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19459
UR  - https://arxiv.org/abs/2610.19459
AB  - 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.
ER  -