New quantum codes from constacyclic codes over finite chain rings

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