2021/11/01 by Alonso-González, Clementa, Navarro-Pérez, Miguel Ángel, Soler-Escrivà, Xaro
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2111.00910
Given \mathbbFq the finite field with q elements and an integer n≥ 2, a flag is a sequence of nested subspaces of \mathbbFqn and a flag code is a nonempty set of flags. In this context, the distance between flags is the sum of the corresponding subspace distances. Hence, a given flag distance value might be obtained by many different combinations. To capture such a variability, in the paper at hand, we introduce the notion of distance vector as an algebraic object intrinsically associated to a flag code that encloses much more information than the distance parameter itself. Our study of the flag distance by using this new tool allows us to provide a fine description of the structure of flag codes as well as to derive bounds for their maximum possible size once the minimum distance and dimensions are fixed.