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 and Paley graphs in the Galois field $$GF(p^{r})$$GF(pr), where $$p\in {\mathbb {P}}$$p?P and $$r\in {\mathbb {Z}}^{+}$$r?Z+. The parameters of two new classes of quantum codes are $$[[(2k'+2)(8k'+7),2(8k'^{2}+7k'),d_\mathrm{min}]]$$[[(2k?+2)(8k?+7),2(8k?2+7k?),dmin]] and $$[[(2k'+2)(8k'+9),2(8k'^{2}+9k'+1),d_\mathrm{min}]]$$[[(2k?+2)(8k?+9),2(8k?2+9k?+1),dmin]], respectively, where $$d_\mathrm{min}\ge 3$$dmin?3. For these quantum codes, the code rate approaches 1 as $$k'$$k? tends to infinity.
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