S. Marcugini

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...