English

New Qubit Codes from Multidimensional Circulant Graphs

Information Theory 2023-09-06 v1 math.IT

Abstract

Two new qubit stabilizer codes with parameters [77,0,19]2[77, 0, 19]_2 and [90,0,22]2[90, 0, 22]_2 are constructed for the first time by employing additive symplectic self-dual \F4\F_4 codes from multidimensional circulant (MDC) graphs. We completely classify MDC graph codes for lengths 4n404\le n \le 40 and show that many optimal \dsb,0,d\dsb{\ell, 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.

Keywords

Cite

@article{arxiv.2309.01798,
  title  = {New Qubit Codes from Multidimensional Circulant Graphs},
  author = {Padmapani Seneviratne and Hannah Cuff and Alexandra Koletsos and Kerry Seekamp and Adrian Thnanopavarn},
  journal= {arXiv preprint arXiv:2309.01798},
  year   = {2023}
}
R2 v1 2026-06-28T12:12:32.162Z