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- W4378474377 abstract "A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically good codes, we explicitly construct strong blocking sets in the $(k-1)$-dimensional projective space over $mathbb{F}_q$ that have size $O( q k )$. Since strong blocking sets have recently been shown to be equivalent to minimal linear codes, our construction gives the first explicit construction of $mathbb{F}_q$-linear minimal codes of length $n$ and dimension $k$, for every prime power $q$, for which $n = O (q k)$. This solves one of the main open problems on minimal codes." @default.
- W4378474377 created "2023-05-27" @default.
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- W4378474377 date "2023-05-24" @default.
- W4378474377 modified "2023-09-25" @default.
- W4378474377 title "Strong blocking sets and minimal codes from expander graphs" @default.
- W4378474377 doi "https://doi.org/10.48550/arxiv.2305.15297" @default.
- W4378474377 hasPublicationYear "2023" @default.
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