New quantum codes from constacyclic codes over finite chain rings

Let R be the finite chain ring \(\mathbb {F}_{p^{2m}}+{u}\mathbb {F}_{p^{2m}}\) ${\mathbb{F}}_{p^{2m}}+u{\mathbb{F}}_{p^{2m}}$ , where \(\mathbb {F}_{p^{2m}}\) ${\mathbb{F}}_{p^{2m}}$ is the finite field with \(p^{2m}\) $p^{2m}$ elements, p is a prime, m is a non-negative integer and \({u}^{2}=0.\) $u^2=0.$ In this paper, we firstly define a class of Gray maps, which changes the Hermitian self-orthogonal property of linear codes over \(\mathbb {F}_{2^{2m}}+{u}\mathbb {F}_{2^{2m}}\) ${\mathbb{F}}_{2^{2m}}+u{\mathbb{F}}_{2^{2m}}$ into the Hermitian self-orthogonal property of linear codes over \(\mathbb {F}_{2^{2m}}\) ${\mathbb{F}}_{2^{2m}}$ . Applying the Hermitian construction, a new class of \(2^{m}\) $2^m$ -ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over \(\mathbb {F}_{2^{2m}}+{u}\mathbb {F}_{2^{2m}}.\) ${\mathbb{F}}_{2^{2m}}+u{\mathbb{F}}_{2^{2m}}.$ We secondly define another class of maps, which changes the Hermitian self-orthogonal property of linear codes over R into the trace self-orthogonal property of linear codes over \(\mathbb {F}_{p^{2m}}\) ${\mathbb{F}}_{p^{2m}}$ . Using the Symplectic construction, a new class of \(p^{m}\) $p^m$ -ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over R.