2014/01/01 by Nicolas Delfosse, Zhentao Li, Stéphan Thomassé
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Cayley graph #Error Correcting Code Techniques #Hypercube #Low-density parity-check code #Minimum distance #Parity (physics) #Quadratic equation #Quantum #Quantum Computing Algorithms and Architecture #Upper and lower bounds #cs.IT #graph theory and CDMA systems #math.CO #math.IT #quant-ph
paper · pdf · doi:10.1007/978-3-662-44465-8_21
published in Lecture notes in computer science, 239-250 (Springer Science+Business Media)
openalex publication_date 2014/01/01 · arxiv created 2014/04/25 · arxiv updated 2016/01/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We provide a new lower bound on the minimum distance of a family of quantum LDPC codes based on Cayley graphs proposed by MacKay, Mitchison and Shokrollahi. Our bound is exponential, improving on the quadratic bound of Couvreur, Delfosse and Zémor. This result is obtained by examining a family of subsets of the hypercube which locally satisfy some parity conditions.