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"origin": "submission", "novelty": "new_parameters", "construction": "Two-sheeted cyclic cover of the {4,5} surface code [[360,38,8]] of the orientably-regular map R19.3 (M. Conder's list of reflexible maps of genus 2 to 301, genus 19; the board entry 360-38-8 is this base code). Base group G = of order 720; darts = elements of G (right multiplication), faces g, vertices g, edges g = {g, grs}. Voltage omega in Z/2 on the base edges, equal to 1 exactly on the 41 edges {w, w*r*s} for w in: r^-1*s^-1; s*r^-1; s^-2; r^-1*s^-2; s^-2*r; r*s^-2*r*s^-1; r^-1*s*r^-1*s^-1*r; s^-2*r*s^-1*r; r^2*s^-2*r*s^-1; r*s*r^-1*s^-1*r*s^-1; r*s^2*r^-1*s*r^-1; s*r^-1*s^-1*r*s^-2; s^-1*r*s^-2*r*s^-1; r^2*s^2*r^-1*s*r^-1; r*s*r^-1*s*r^-1*s^-2; r*s^-1*r*s*r^-1*s*r^-1; r^-1*s*r^-1*s^-1*r*s^-1*r; s^-2*r*s^-1*r*s^-1*r; r^2*s*r^-1*s^-1*r*s^-1*r; r^2*s^-1*r*s*r^-1*s*r^-1; r^2*s^-1*r*s*r^-1*s^-2; r^2*s^-1*r*s^-1*r*s^-2; r*s*r^-1*s^-1*r*s^-2*r; r^-1*s*r^-1*s^-1*r*s^-1*r*s^-1; s*r^-1*s^-1*r*s^-1*r*s*r^-1; s^-1*r*s^2*r^-1*s*r^-1*s^-1; s^-1*r*s^-1*r*s*r^-1*s*r^-1; s^-1*r*s^-1*r*s*r^-1*s^-2; r^2*s*r^-1*s*r^-1*s^-1*r*s^-1; r^2*s*r^-1*s^2*r^-1*s*r^-1; r^2*s*r^-1*s^-1*r*s^-1*r*s^-1; r*s*r^-1*s*r^-1*s*r^-1*s^-1*r; r*s^-1*r*s^-1*r*s^-2*r*s^-1; r^-1*s*r^-1*s*r^-1*s^-2*r*s^-1; r^-1*s^-1*r*s*r^-1*s*r^-1*s^-2; s*r^-1*s*r^-1*s^-2*r*s^-1*r; r^2*s^-1*r*s^-1*r*s^-1*r*s*r^-1; r^2*s^-1*r*s^-1*r*s^-1*r*s^-2; r*s*r^-1*s*r^-1*s*r^-1*s^-1*r*s^-1; r*s^2*r^-1*s*r^-1*s^-2*r*s^-1; r^-1*s^-1*r*s*r^-1*s*r^-1*s*r^-1*s^-1. Cover darts (g,i), g in G, i in Z/2, with R~(g,i) = (g r, i + omega(g)) and S~(g,i) = (g s, i), omega(g) the voltage of the edge through g; faces, vertices and edges are the cycles of R~, S~ and R~S~: (V,E,F) = (288,720,360), genus 37. Qubits on the 720 edges, X-checks on the 288 vertices (weight 5), Z-checks on the 360 faces (weight 4), incidences mod 2, so k = 2 - chi = 74. Not a regular map (no orientably-regular {4,5} map of genus 37 exists). The qubit order is that of the public package in the references (data/maps.json: base darts and a cohomologous voltage with 87 edges), whose src/rebuild.py rebuilds these matrices and checks the isomorphism with the cover above.", "references": [ "https://arxiv.org/abs/1506.04029", "https://www.math.auckland.ac.nz/~conder/RegularOrientableMaps301.txt", "https://github.com/TimoKellerMath/quantum-error-correction/tree/2e97a5361e7b9327128baa242bdedd333f7d7e12/hyperbolic-map-codes" ], "date": "2026-11-10", "model": "Claude Opus 5.5", "notes": "Exact distance d_X = d_Z = 8: tropidist (arXiv:2611.08247) at the board's pinned commit b03ec2d4077f closes both sides (certs/720-74-8.json, level solver); independently two exact programs for check matrices with column weight 2 and an enumeration of all circuits of length <= 8 (100 X-type and 6108 Z-type logical operators of weight 8, none lighter), see the research note. Novelty: no board entry with these n and k at commit 8042f9da; parameters not found in Breuckmann and Terhal (arXiv:1506.04029), Breuckmann et al. (arXiv:1703.00590), Breuckmann's thesis (arXiv:1802.01520), Mahmoud and Rayan (arXiv:2610.10948), Breuckmann and Burton (arXiv:2202.06647), Mahmoud, Ali and Rayan (arXiv:2504.07800), the catalogs of QEC-pages (Quantum_LDPC_Codes) and qecdb.org; Conder's lists contain the map, not the code. Equivalence with existing entries: checked, none has these n and k." }, "family": "topological" }