New quantum codes from constacyclic codes over finite chain rings

Let R be the finite chain ring F_p²ᵐ+uF_p²ᵐ, where F_p²ᵐ is the finite field with p²ᵐ elements, p is a prime, m is a non-negative integer and u²=0. In this paper, we firstly define a class of Gray maps, which changes the Hermitian self-orthogonal property of linear codes over F_2²ᵐ+uF_2²ᵐ into the Hermitian self-orthogonal property of linear codes over F_2²ᵐ. Applying the Hermitian construction, a new class of 2ᵐ-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over F_2²ᵐ+uF_2²ᵐ. 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 F_p²ᵐ. Using the Symplectic construction, a new class of pᵐ-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over $R.$