Author

S. Marcugini

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Preprint Sep 2026

Further results on binary linear covering codes and saturating sets in projective spaces

The binary length function $\ell_2(r,R)$ is the smallest length of a binary linear code with codimension (redundancy) $r$ and covering radius $R$. Let $s_2(N,\rho)$ be the smallest size of a $\rho$-saturating set in the binary projective space $\mathrm{PG}(N,2)$. It is known that the binary length function satisfies $\...

A. Davydov, S. Marcugini, F. Pambianco et al. · 0 citations

Sep 2026

Further results on binary codes of covering radius 2 and saturating sets in projective spaces

The length function $\ell_2(r,R)$ is the smallest length of a binary linear code with codimension (redundancy) $r$ and covering radius $R$. Let $s_2(N,\rho)$ be the smallest size of a $\rho$-saturating set in the projective space $\mathrm{PG}(N,2)$. It is known that $\ell_2(r,R)=s_2(r-1,R-1)$. We obtain the following n...

A. Davydov, S. Marcugini, F. Pambianco et al. · arXiv.org · 1 citation · ⚡1