Binary Caps and LCD Codes with Large Dimensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917383997751296 |
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| author | Ishizuka, Keita Kamio, Yuhi |
| author_facet | Ishizuka, Keita Kamio, Yuhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03734 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Binary Caps and LCD Codes with Large Dimensions Ishizuka, Keita Kamio, Yuhi Information Theory Combinatorics 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. |
| title | Binary Caps and LCD Codes with Large Dimensions |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2604.03734 |