Topological quantum codes from self-complementary self-dual graphs

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)”, where p ∈ P and r ∈ Z. The parameters of two new classes of quantum codes are [[(2k + 2)(8k + 7), 2(8k +7k), dmin]] and [[(2k+2)(8k +9), 2(8k +9k +1), dmin]] respectively, where dmin ≥ 3. For these quantum codes, the code rate approaches 1 as k goes to infinity.