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math.CO2025
The maximum number of nonzero weights of linear rank-metric codes
Chiara Castello, Paolo Santonastaso, Martin Scotti
We investigate the maximum number \( L_{\mathrm{rk}}(n, m, k, q) \) of distinct nonzero rank weights that an \( \mathbb{F}_{q^m} \)-linear rank-metric code of dimension \( k \) in…
math.CO2025
Linear rank-metric intersecting codes
Daniele Bartoli, Martino Borello, Giuseppe Marino +1
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecti…
math.CO2024
The geometry of intersecting codes and applications to additive combinatorics and factorization theory
Martino Borello, Wolfgang Schmid, Martin Scotti
Intersecting codes are linear codes where every two nonzero codewords have non-trivially intersecting support. In this article we expand on the theory of this family of codes, by s…