Flag codes from planar spreads in network coding Articles uri icon

authors

  • ALONSO-GONZÁLEZ, CLEMENTA
  • NAVARRO PEREZ, MIGUEL ANGEL
  • SOLER-ESCRIVA, XARO

publication date

  • December 2020

start page

  • 1

end page

  • 20

volume

  • 68, 101745

International Standard Serial Number (ISSN)

  • 1071-5797

Electronic International Standard Serial Number (EISSN)

  • 1090-2465

abstract

  • In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space , being q a prime power and the finite field of q elements. In particular, we focus on flag codes having maximum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For, we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of them as well as a decoding algorithm.

subjects

  • Mathematics

keywords

  • network coding; subspace codes; projective space; spreads; flag codes