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Symplectic isometries of stabilizer codes
Preview AbstractIn this paper, we study the equivalence of quantum stabilizer codes via symplectic isometries of stabilizer codes. We define monomially and symplectically equivalent stabilizer codes and determine how different the two notions can be. Further, we show that monomial maps correspond to local Clifford operators. We relate the latter with the LU-LC Conjecture.
Quantum codes over rings
Preview AbstractThis paper considers the construction of quantum error correcting codes from linear codes over finite commutative Frobenius rings. We extend the Calderbank–Shor–Steane (CSS) construction to these rings. Further, quantum codes are extended to matrix product codes. Quantum codes over 𝔽pk are also obtained from linear codes over rings using the generalized Gray map.