Noisy-Syndrome Decoding of Hypergraph Product Codes

• URL: http://arxiv.org/abs/2510.07602v1
• Date: Wed, 08 Oct 2025 22:48:39 GMT
• Title: Noisy-Syndrome Decoding of Hypergraph Product Codes
• Authors: Venkata Gandikota, Elena Grigorescu, Vatsal Jha, S. Venkitesh,
• Abstract summary: Hypergraph product codes are a prototypical family of quantum codes with state-of-the-art decodability properties.<n>In this work we consider the "noisy" syndrome decoding problem for hypergraph product codes, and show a similar reduction in the noisy setting.<n>Our results hold for a general family of codes wherein the code and the dual code are "simultaneously nice"; in particular, for codes admitting good syndrome decodability and whose duals look "similar"
• Score: 12.642852068495197
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hypergraph product codes are a prototypical family of quantum codes with state-of-the-art decodability properties. Recently, Golowich and Guruswami (FOCS 2024) showed a reduction from quantum decoding to syndrome decoding for a general class of codes, which includes hypergraph product codes. In this work we consider the "noisy" syndrome decoding problem for hypergraph product codes, and show a similar reduction in the noisy setting, addressing a question posed by Golowich and Guruswami. Our results hold for a general family of codes wherein the code and the dual code are "simultaneously nice"; in particular, for codes admitting good syndrome decodability and whose duals look "similar". These include expander codes, Reed-Solomon codes, and variants.

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