New Qubit Codes from Multidimensional Circulant Graphs
Information Theory
2023-09-06 v1 math.IT
Abstract
Two new qubit stabilizer codes with parameters and are constructed for the first time by employing additive symplectic self-dual codes from multidimensional circulant (MDC) graphs. We completely classify MDC graph codes for lengths and show that many optimal 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.
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}
}