Classical and quantum Coxeter codes: Extending the Reed-Muller family

• URL: http://arxiv.org/abs/2502.14746v1
• Date: Thu, 20 Feb 2025 17:16:28 GMT
• Title: Classical and quantum Coxeter codes: Extending the Reed-Muller family
• Authors: Nolan J. Coble, Alexander Barg,
• Abstract summary: We introduce a class of binary linear codes that generalizes the Reed-Muller family by replacing the group $mathbbZm$ with an arbitrary finite Coxeter group. We also construct quantum CSS codes arising from the Coxeter codes, which admit logical operators outside of the Clifford group.
• Score: 59.90381090395222
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• Abstract: We introduce a class of binary linear codes that generalizes the Reed-Muller family by replacing the group $\mathbb{Z}_2^m$ with an arbitrary finite Coxeter group. Similar to the Reed-Muller codes, this class is closed under duality and has rate determined by a Gaussian distribution. We also construct quantum CSS codes arising from the Coxeter codes, which admit transversal logical operators outside of the Clifford group.

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