The Sidon space was introduced in 2017 by Bachoc, Serra, and Z\’emor as the $q$ analogue of the Sidon set. Interest in the Sidon space grew rapidly, especially after his 2018 Roth, Raviv and Tamo study. So far, the known constructions of Sidon spaces fall into three families: those contained in the sum of two multiplicative cosets of fixed subfields of $\mathbb{F}_{q^n}$ , The sum of two or more multiplicative cosets of the fixed subfields of $\mathbb{F}_{q^n}$, and finally what you get as the kernel of the subspace polynomials. In this paper, we mainly focus on the first class of examples, provide characterization results, and show some new examples arising from some well-known combinatorial objects. Furthermore, we give a very natural definition of equivalence between sidon spaces, which relies on the notion of equivalence in cyclic subspace codes, and discuss the equivalence of known examples.

Source link


Leave A Reply