Year: 2026
Type: preprint
Abstract: The hull of a linear code is the intersection of the code with its dual and depends on the choice of inner product. We study how the numbers of linear codes with prescribed Euclidean, Hermitian, and symplectic hull dimensions vary with the hull dimension. Building on closed enumeration formulae, we derive exact ratio decompositions for the Hermitian and symplectic cases, determine the parameter ranges in which monotonicity holds, and identify the exceptional families. We also compare the three inner products and complement the theoretical analysis with computational classification results for quaternary codes.
Source: arXiv (Cornell University)
Institution: Mitsubishi Electric (Japan)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: グラフの不変量と符号の不変量の関連の解明
OpenAlex ID: W7162765427