Quantum codes from Hermitian dual-containing constacyclic codes over $${\mathbb {F}}_{q^{2}}+{v}{\mathbb {F}}_{q^{2}}$$ F q 2 + v F q 2
Quantum Information Processing(2021)
摘要
Let
$${\mathbb {R}}$$
be the finite non-chain ring
$${\mathbb {F}}_{{ q}^{2}}+{v}{\mathbb {F}}_{{ q}^{2}}$$
, where
$${v}^{2}={v}$$
and q is an odd prime power. In this paper, we study quantum codes over
$${\mathbb {F}}_{{ q}}$$
from constacyclic codes over
$${\mathbb {R}}$$
. We define a class of Gray maps, which preserves the Hermitian dual-containing property of linear codes from
$${\mathbb {R}}$$
to
$${\mathbb {F}}_{{ q}^{2}}$$
. We study
$${\alpha }(1-2v)$$
-constacyclic codes over
$${\mathbb {R}}$$
, and show that the images of
$$\alpha (1-2v)$$
-constacyclic codes over
$${\mathbb {R}}$$
under the special Gray map are
$$\alpha ^{2}$$
-constacyclic codes over
$${\mathbb {F}}_{{ q}^{2}}$$
. Some new non-binary quantum codes are obtained via the Gray map and the Hermitian construction from Hermitian dual-containing
$$\alpha (1-2v)$$
-constacyclic codes over
$${\mathbb {R}}$$
.
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关键词
Quantum codes,Constacyclic codes,Hermitian dual-containing,Gray map
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