6 papers · 1 filter
Uniform Sampling of Linear Codes with Prescribed Hull Dimension
Keita Ishizuka
We give exactly uniform samplers for linear codes with prescribed hull dimension, for the Euclidean, Hermitian, and symplectic inner products and over finite fields of every charac…
Classification of binary, ternary and quaternary Hermitian LCD codes
Keita Ishizuka
We extend the complete classifications of linear complementary dual (LCD) codes from length 15 to length 19 in the binary case, from length 10 to length 15 in the ternary case and…
Enumeration and Monotonicity of Linear Codes with Prescribed Hull Dimensions
Stefka Bouyuklieva, Keita Ishizuka, Iliya Bouyukliev +1
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 Euclide…
The Closure of LCD-to-GI Reductions via Generalized Inner Products
Keita Ishizuka
The Permutation Equivalence Problem (PEP) for linear complementary dual (LCD) codes reduces to Graph Isomorphism (GI) through the orthogonal projector onto the code, but this requi…
Caps and LCD Codes with Large Dimensions
Keita Ishizuka, Yuhi Kamio
We establish a connection between linear complementary dual (LCD) codes and caps in projective space. Using this framework and the structure theory of maximal binary caps, we deriv…
Almost All Vectorial Functions Have Trivial Extended-Affine Stabilizers
Keita Ishizuka
We prove that asymptotically almost all vectorial functions over finite fields have trivial extended-affine stabilizers. As a consequence, the number of EA-equivalence classes is a…