Optimum distance flag codes from spreads via perfect matchings in graphs Articles uri icon

publication date

  • December 2021

start page

  • 1279

end page

  • 1297

issue

  • 4

volume

  • 54

International Standard Serial Number (ISSN)

  • 0925-9899

abstract

  • In this paper, we study flag codes on the vector space Fnq , being q a prime power and Fq the finite field of q elements. More precisely, we focus on flag codes that attain the maximum possible distance (optimum distance flag codes) and can be obtained from a spread of Fnq . We characterize the set of admissible type vectors for this family of flag codes and also provide a construction of them based on well-known results about perfect matchings in graphs. This construction attains both the maximum distance for its type vector and the largest possible cardinality for that distance.

subjects

  • Mathematics

keywords

  • network coding; subspace codes; spreads; flag codes; graphs; perfect matching