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New Qubit Codes from Multidimensional Circulant Graphs

2023/09/04 by Seneviratne, Padmapani, Cuff, Hannah, Koletsos, Alexandra +2
#94B05 #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2309.01798

Abstract

Two new qubit stabilizer codes with parameters [77, 0, 19]2 and [90, 0, 22]2 are constructed for the first time by employing additive symplectic self-dual \F4 codes from multidimensional circulant (MDC) graphs. We completely classify MDC graph codes for lengths 4≤ n ≤ 40 and show that many optimal \dsbℓ, 0, d qubit codes can be obtained from the MDC construction. Moreover, we prove that adjacency matrices of MDC graphs have nested block circulant structure and determine isomorphism properties of MDC graphs.

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