Exact lengths of shortest t-dimensional hull embeddings for linear codes are derived via quadratic form theory and group theory, with algorithms that classify codes by Gram matrix types and yield new optimal codes.
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Closed-form ratio decompositions for linear codes with fixed Hermitian and symplectic hull dimensions over finite fields, with uniform lower bound 2/3 for Hermitian and asymptotic decay to 1/q² for symplectic, implying monotonicity for quantum code constructions.
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Shortest Embeddings of Linear Codes with Arbitrary Hull Dimension
Exact lengths of shortest t-dimensional hull embeddings for linear codes are derived via quadratic form theory and group theory, with algorithms that classify codes by Gram matrix types and yield new optimal codes.
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Comparative monotonicity of linear codes by Hermitian and symplectic hull dimensions
Closed-form ratio decompositions for linear codes with fixed Hermitian and symplectic hull dimensions over finite fields, with uniform lower bound 2/3 for Hermitian and asymptotic decay to 1/q² for symplectic, implying monotonicity for quantum code constructions.