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arXiv · 2606.11987

Graphical Analysis of Lifted Product Code Constructions

Ragnar Freij-Hollanti·Kirsten D. Morris·Patricija Šapokaitė
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Abstract

Lifted product codes are an important family of quantum low-density parity-check (QLDPC) codes, as they were the first QLDPC code family shown to be asymptotically good. Understanding the structure of their parity-check matrices $H_{\mathsf{X}}$ and $H_{\mathsf{Z}}$, as well as the associated Tanner graphs, is essential for analyzing their decoding behavior and error-floor performance. In this work, we show that the Tanner graphs of $H_{\mathsf{X}}$ and $H_{\mathsf{Z}}$ are indeed isomorphic, and investigate their graph-theoretical structure. We establish conditions ensuring the connectivity of these graphs and provide bounds on their minimal absorbing sets, providing new insight into the combinatorial structures influencing decoding performance.

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Ragnar Freij-Hollanti, Kirsten D. Morris, Patricija Šapokaitė. 2026-06-10. Graphical Analysis of Lifted Product Code Constructions. https://arxiv.org/abs/2606.11987

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