We use symplectic self-dual additive codes over $ \mathbb{F}_4 $ obtained from metacirculant graphs to construct, for the first time, $ \left[\kern-0.15em\left[ {\ell, 0, d} \right]\kern-0.15em\right] $ qubit codes with parameters $ (\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\} $. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.

Advances in Mathematics of CommunicationsJan 12, 20221 citation

arXiv:1509.04846 · Discrete Mathematics

New self-dual additive F4 -codes constructed from circulant graphs

Markus Grassl, Masaaki Harada

Published Nov 14, 2016• 11 citations

arXiv HTML PDF

DOI: 10.1016/j.disc.2016.08.023

Related papers

New quantum codes constructed from some self-dual additive F4 -codes

Masaaki Harada

arXiv:1805.12229Information Processing LettersMay 30, 20186 citations

Formally self-dual additive codes over F4

Sunghyu Han, Jon-Lark Kim

Journal of Symbolic ComputationMar 26, 201012 citations

On self-dual and LCD double circulant and double negacirculant codes over F q + uF q .

Minjia Shi, Hongwei Zhu, Liqin Qian +2 more

Jan 1, 20188 citations

Performance of ternary double circulant, double twistulant, and self-dual codes

Thomas Aaron Gulliver, Masaaki Harada

arXiv:1609.01809Applicable Algebra in Engineering Communication and ComputingJan 16, 20170 citations

Properties and Comparisons of Various Graphs and Their Codes

Andreas Garcia, Layla Jarrahy, Elisaveta Samoylov

It is established in literature that finding stabilizer quantum error correcting codes (QECCS) is the same as finding self-dual additive codes over the finite field $\mathbb{F}_{4}$ under the Hermitian trace inner product. Additionally, every self-dual additive code can be represented by a graph adjacency matrix. Many selfdual additive codes are constructed from circulant graphs. We introduce new graph code constructions: the Toeplitz Graph, the Multidimensional Toeplitz Graph (MDT), and the Generalized Toeplitz (GT) graph constructions. We consider some of the properties of the Toeplitz and Multidimensional Toeplitz Graphs and compare the Circulant and GT code constructions.It is established in literature that finding stabilizer quantum error correcting codes (QECCS) is the same as finding self-dual additive codes over the finite field $\mathbb{F}_{4}$ under the Hermitian trace inner product. Additionally, every self-dual additive code can be represented by a graph adjacency matrix. Many selfdual additive codes are constructed from circulant graphs. We introduce new graph code constructions: the Toeplitz Graph, the Multidimensional Toeplitz Graph (MDT), and the Generalized Toeplitz (GT) graph constructions. We consider some of the properties of the Toeplitz and Multidimensional Toeplitz Graphs and compare the Circulant and GT code constructions.

IEEE MIT Undergraduate Research Technology Conference (URTC)Oct 11, 20240 citations

New quantum codes from metacirculant graphs via self-dual additive $\mathbb{F}_4$ -codesNew quantum codes from metacirculant graphs via self-dual additive $\mathbb{F}_4$-codes

Padmapani Seneviratne, Martianus Frederic Ezerman

Advances in Mathematics of CommunicationsJan 12, 20221 citation

It is established in literature that finding stabilizer quantum error correcting codes (QECCS) is the same as finding self-dual additive codes over the finite field

\mathbb{F}_{4}

under the Hermitian trace inner product. Additionally, every self-dual additive code can be represented by a graph adjacency matrix. Many selfdual additive codes are constructed from circulant graphs. We introduce new graph code constructions: the Toeplitz Graph, the Multidimensional Toeplitz Graph (MDT), and the Generalized Toeplitz (GT) graph constructions. We consider some of the properties of the Toeplitz and Multidimensional Toeplitz Graphs and compare the Circulant and GT code constructions.

New quantum codes from metacirculant graphs via self-dual additive

\mathbb{F}_4

-codes