Binary Caps and LCD Codes with Large Dimensions

Keita Ishizuka; Yuhi Kamio

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arXiv · 2604.03734

Binary Caps and LCD Codes with Large Dimensions

Keita Ishizuka·Yuhi Kamio

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Abstract

We establish a connection between linear complementary dual (LCD) codes and caps in projective space. Using this framework and the structure theory of maximal caps, we derive nonexistence theorems for LCD codes with minimum distance at least $4$, providing computation-free proofs that were previously obtained only through exhaustive search. As an application, we completely determine the optimal minimum distances for codimensions $7$ and $8$ for the first time.

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Keita Ishizuka, Yuhi Kamio. 2026-04-04. Binary Caps and LCD Codes with Large Dimensions. https://arxiv.org/abs/2604.03734

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