Small quantum Tanner codes from left--right Cayley complexes

• URL: http://arxiv.org/abs/2512.20532v1
• Date: Tue, 23 Dec 2025 17:23:31 GMT
• Title: Small quantum Tanner codes from left--right Cayley complexes
• Authors: Anthony Leverrier, Wouter Rozendaal, Gilles Zémor,
• Abstract summary: Quantum Tanner codes provably display a linear minimum distance and a constant encoding rate in the limit.<n>We compute the dimension of quantum Tanner codes when the right degree of the complex is 2.<n>We identify instances of quantum Tanner codes with parameters $[144,12,11]]$, $[432,20,leq 22]]$ and $[576,28,leq 24]]$ for generators of weight 9.
• Score: 11.113224276505562
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum Tanner codes are a class of quantum low-density parity-check codes that provably display a linear minimum distance and a constant encoding rate in the asymptotic limit. When built from left--right Cayley complexes, they can be described through a lifting procedure and a base code, which we characterize. We also compute the dimension of quantum Tanner codes when the right degree of the complex is 2. Finally, we perform an extensive search over small groups and identify instances of quantum Tanner codes with parameters $[[144,12,11]]$, $[[432,20,\leq 22]]$ and $[[576,28,\leq 24]]$ for generators of weight 9.

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