Waring identifiable subspaces over finite fields

2022/07/27 by Michel Lavrauw, Ferdinando Zullo, Lavrauw, Michel +1
Computer Science · Mathematics · #Coding theory and cryptography #Tensor decomposition and applications #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2207.13456

Abstract

Waring's problem, of expressing an integer as the sum of powers, has a very long history going back to the 17th century, and the problem has been studied in many different contexts. In this paper we introduce the notion of a Waring subspace and a Waring identifiable subspace with respect to a projective algebraic variety \mathcal X. When \mathcal X is the Veronese variety, these subspaces play a fundamental role in the theory of symmetric tensors and are related to the Waring decomposition and Waring identifiability of symmetric tensors (homogeneous polynomials). We give several constructions and classification results of Waring identifiable subspaces with respect to the Veronese variety in ℙ⁵(\mathbbF_q) and in ℙ⁹(\mathbbF_q), and include some applications to the theory of linear systems of quadrics in ℙ³(\mathbbF_q).

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