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- Title
Topological quantum codes from self-complementary self-dual graphs.
- Authors
Naghipour, Avaz; Jafarizadeh, Mohammad; Shahmorad, Sedaghat
- Abstract
In this paper, we present two new classes of binary quantum codes with minimum distance of at least three, by self-complementary self-dual orientable embeddings of 'voltage graphs' and 'Paley graphs in the Galois field $$GF(p^{r})$$ ', where $$p\in {\mathbb {P}}$$ and $$r\in {\mathbb {Z}}^{+}$$ . The parameters of two new classes of quantum codes are $$[[(2k'+2)(8k'+7),2(8k'^{2}+7k'),d_\mathrm{min}]]$$ and $$[[(2k'+2)(8k'+9),2(8k'^{2}+9k'+1),d_\mathrm{min}]]$$ , respectively, where $$d_\mathrm{min}\ge 3$$ . For these quantum codes, the code rate approaches 1 as $$k'$$ tends to infinity.
- Subjects
QUANTUM theory; TOPOLOGY; EMBEDDINGS (Mathematics); SET theory; GRAPH theory
- Publication
Quantum Information Processing, 2015, Vol 14, Issue 11, p4057
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-015-1115-9