An orbital construction of optimum distance flag codes Articles uri icon

publication date

  • August 2021

start page

  • 1

end page

  • 21

issue

  • 101861

volume

  • 73

International Standard Serial Number (ISSN)

  • 1071-5797

abstract

  • Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space , where q is a prime power and , the finite field of size q. In this paper we study the construction on of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension k and maximum distance with a given orbital description, we provide sufficient conditions to get an optimum distance full flag code on having an orbital structure directly induced by the previous one. In particular, we exhibit a specific orbital construction with the best possible size from an orbital construction of a planar spread on that strongly depends on the characteristic of the field.

subjects

  • Mathematics

keywords

  • network coding; spreads; subspace codes; orbit codes; flag codes; general linear group