Over fields of characteristic unequal to 2, we can identify symmetric matrices with homogeneous polynomials of degree 2. This allows us to view symmetric rank-metric codes as living inside the space of such polynomials.
Mar 12, 2023
In this paper, we generalize the construction of symmetric Delsarte–Gabidulin codes to polynomials of degree over fields of characteristic 0 or .
Sep 11, 2024 · This allows us to view symmetric rank-metric codes as living inside the space of such polynomials. In this paper, we generalize the construction ...
Nov 25, 2024 · Abstract. Over fields of characteristic unequal to 2, we can identify symmetric matrices with homogeneous polynomials of degree 2.
Field F. F = Fq. V finite dimensional F-vector space. wt : V → N weight function. δ : V × V → R≥0; δ(u,v) := wt(u − v) distance function.
Mar 12, 2023 · This is an equivalent framework in which one can study symmetric rank-metric codes. The goal of this paper is to extend the study of symmetric ...
We provide bounds on the minimal distance and dimension of the essential-rank metric codes we construct and provide an efficient decoding algorithm. Finally, we ...
Nov 28, 2024 · Using the theory of association schemes, bounds, constructions, and structural properties of restricted rank metric codes have been ...
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"Higher-degree symmetric rank-metric codes" A new preprint by Arthur Bik and Alessandro Neri is online on arXiv! https://arxiv.org/abs/2303.06745.
Higher-degree symmetric rank-metric codes · A. BikAlessandro Neri. Mathematics. ArXiv. 2023. TLDR. This paper generalizes the construction of symmetric ...