Speaker
Valentino Smaldore
(Università degli Studi di Padova)
Description
Let $\mathcal{C} = \{c_0, c_1, \ldots, c_{q^k}\} \subseteq \mathbb{F}_q^n$ be a $[n,k]_q$-linear code endowed with the Hamming metric. That is, $\mathcal{C}$ is a $k$-subspace of $\mathbb{F}_q^n$. Let $M_{\mathcal{C}}\in\mathbb{R}^{q^k\times q^k}$ be the distance matrix of the code defined as $(M_\mathcal{C})_{i,j} := d_H(c_i, c_j)=|\{i\colon x_i\neq y_i\}|$. We analyze the spectrum of $M_{\mathcal{C}}$, providing examples of spectra for well-known families of linear codes. We compute the multiset of the eigenvalues of $M_{\mathcal{C}}$ and bases for their respective eigenspaces.
Authors
Mr
Adrián Fidalgo-Diaz
(Universidad de Valladolid)
Mr
Gonzalo Rodríguez Pajares
(Universidad de Valladolid)
Valentino Smaldore
(Università degli Studi di Padova)