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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.15372 |
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| _version_ | 1866908665550733312 |
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| author | Adriaensen, Sam Sziklai, Peter Weiner, Zsuzsa |
| author_facet | Adriaensen, Sam Sziklai, Peter Weiner, Zsuzsa |
| contents | In a 2022, Bartoli, Cossidente, Marino, and Pavese proved that in the projective space ${\rm PG}(3,q^3)$, one can find three $\mathbb F_q$-subgeometries such that the union of their point sets is a strong blocking set. This proves the existence of linear minimal codes with parameters $[3(q^2+1)(q+1),4]_{q^3}$ for every prime power $q$. We give a short proof of this result for odd values of $q > 9$, using the theory of small blocking sets in projective planes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on short minimal codes from subgeometries Adriaensen, Sam Sziklai, Peter Weiner, Zsuzsa Combinatorics 51E21, 94B27 In a 2022, Bartoli, Cossidente, Marino, and Pavese proved that in the projective space ${\rm PG}(3,q^3)$, one can find three $\mathbb F_q$-subgeometries such that the union of their point sets is a strong blocking set. This proves the existence of linear minimal codes with parameters $[3(q^2+1)(q+1),4]_{q^3}$ for every prime power $q$. We give a short proof of this result for odd values of $q > 9$, using the theory of small blocking sets in projective planes. |
| title | A note on short minimal codes from subgeometries |
| topic | Combinatorics 51E21, 94B27 |
| url | https://arxiv.org/abs/2511.15372 |