Flag codes: Distance vectors and cardinality bounds Articles uri icon

publication date

  • January 2023

start page

  • 27

end page

  • 62

volume

  • 656

International Standard Serial Number (ISSN)

  • 0024-3795

Electronic International Standard Serial Number (EISSN)

  • 1873-1856

abstract

  • Given the finite field with q elements and an integer, a flag is a sequence of nested subspaces of 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.

subjects

  • Mathematics

keywords

  • network coding; flag codes; flag distance; bounds