Explicit constructions of optimal linear codes with Hermitian hulls and their application to quantum codes
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We prove that any Hermitian self-orthogonal [n,k,d]_q^2 code gives rise to an [n,k,d]_q^2 code with ℓ dimensional Hermitian hull for 0≤ℓ≤ k. We present a new method to construct Hermitian self-orthogonal [n,k]_q^2 codes with large dimensions k>n+q-1/q+1. New families of Hermitian self-orthogonal codes with good parameters are obtained; more precisely those containing almost MDS codes. By applying a puncturing technique to Hermitian self-orthogonal codes, MDS [n,k]_q^2 linear codes with Hermitian hull having large dimensions k>n+q-1/q+1 are also derived. New families of MDS, almost MDS and optimal codes with arbitrary Hermitian hull dimensions are explicitly constructed from algebraic curves. As an application, we provide entanglement-assisted quantum error correcting codes with new parameters.
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