Author

Ferdinando Zullo

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Preprint Nov 2026

Few-Weight Linear Sets and Divisibility of Rank-Metric Codes

We study $\mathbb F_q$-linear sets whose positive point weights belong to a prescribed finite set $A$. The integer $e=\gcd(A)$ always divides the rank of the defining subspace, but the divisibility does not by itself imply linearity over $\mathbb F_{q^e}$. We show that it does in a broad parameter range. Let $L_U$ be a...

J. De Beule, Leen Demuys, Ferdinando Zullo et al. · 0 citations

Preprint Aug 2026

Asymptotic Bounds on Generalized Covering Radii of Binary Primitive BCH Codes

Fix integers $e\ge2$ and $r\ge1$. In this paper we study the $r$-th generalized covering radius $\rho_r\left(BCH(e,m)\right)$ of the binary primitive $e$-error-correcting BCH code $BCH(e,m)$. By using an algebraic-geometric reformulation of the covering problem together with an explicit Lang-Weil estimate, we prove tha...

Mao-Sheng Xiong, Chi-Hoi Yip, Ferdinando Zullo · 4 citations · ⚡1

Preprint Oct 2026

Non-additive symmetric rank-metric codes

We study non-additive rank-metric codes contained in the space of symmetric matrices over a finite field. Our main focus is on symmetric $2$-codes. For odd $q$, we introduce a quotient construction for $\mathrm{Sym}_3(q)$ in which rank-one differences are described by isotropic vectors of a nondegenerate quadratic form...

Marta Messia, Ferdinando Zullo · 0 citations