A further study on the mass formula for linear codes with prescribed hull dimension
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Finding a mass formula for a given class of linear codes is a fundamental problem in combinatorics and coding theory. In this paper, we consider the action of the unitary (resp. symplectic) group on the set of all Hermitian (resp. symplectic) linear complementary dual (LCD) codes, prove that all Hermitian (resp. symplectic) LCD codes are on a unique orbit under this action, and determine the formula for the size of the orbit. Based on this, we develop a general technique to obtain a closed mass formula for linear codes with prescribed Hermitian (resp. symplectic) hull dimension, and further obtain some asymptotic results.
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Cited by 2 Pith papers
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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, implyin...
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