Zobrazeno 1 - 10
of 205
pro vyhledávání: '"POLVERINO, Olga"'
For a linear Hamming metric code of length n over a finite field, the number of distinct weights of its codewords is at most n. The codes achieving the equality in the above bound were called full weight spectrum codes. In this paper we will focus on
Externí odkaz:
http://arxiv.org/abs/2405.19911
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association schemes, s
Externí odkaz:
http://arxiv.org/abs/2405.02841
Subspace codes have recently been used for error correction in random network coding. In this work, we focus on one-orbit cyclic subspace codes. If $S$ is an $\mathbb{F}_q$-subspace of $\mathbb{F}_{q^n}$, then the one-orbit cyclic subspace code defin
Externí odkaz:
http://arxiv.org/abs/2405.01652
Sidon spaces have been introduced by Bachoc, Serra and Z\'emor in 2017 as the $q$-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth, Raviv and Tamo in 2018, in which they highlighted the cor
Externí odkaz:
http://arxiv.org/abs/2303.17306
Let $\mathcal{C}\subseteq \mathbb{F}_{q^m}^n$ be an $\mathbb{F}_{q^m}$-linear non-degenerate rank metric code with dimension $k$. In this paper we investigate the problem of determining the number $M(\mathcal{C})$ of codewords in $\mathcal{C}$ with m
Externí odkaz:
http://arxiv.org/abs/2302.00979
A subspace of matrices over $\mathbb{F}_{q^e}^{m\times n}$ can be naturally embedded as a subspace of matrices in $\mathbb{F}_q^{em\times en}$ with the property that the rank of any of its matrix is a multiple of $e$. It is quite natural to ask wheth
Externí odkaz:
http://arxiv.org/abs/2211.08180
Clubs of rank k are well-celebrated objects in finite geometries introduced by Fancsali and Sziklai in 2006. After the connection with a special type of arcs known as KM-arcs, they renewed their interest. This paper aims to study clubs of rank n in P
Externí odkaz:
http://arxiv.org/abs/2209.13339
This paper aims to study linear sets of minimum size in the projective line, that is $\mathbb{F}_q$-linear sets of rank $k$ in $\mathrm{PG}(1,q^n)$ admitting one point of weight one and having size $q^{k-1}+1$. Examples of these linear sets have been
Externí odkaz:
http://arxiv.org/abs/2201.02003
In this paper we consider two pointsets in $\mathrm{PG}(2,q^n)$ arising from a linear set $L$ of rank $n$ contained in a line of $\mathrm{PG}(2,q^n)$: the first one is a linear blocking set of R\'edei type, the second one extends the construction of
Externí odkaz:
http://arxiv.org/abs/2112.11792
Linear sets on the projective line have attracted a lot of attention because of their link with blocking sets, KM-arcs and rank-metric codes. In this paper, we study linear sets having two points of complementary weight, that is with two points for w
Externí odkaz:
http://arxiv.org/abs/2107.10641