Covering of subspaces by subspaces

نویسنده

  • Tuvi Etzion
چکیده

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and a recursive construction. New constructions are given for q = 2 with r = 2 or r = 3. We discuss the density for some of these coverings. Tables for the best known coverings, for q = 2 and 5 ≤ n ≤ 10, are presented. We present some questions concerning possible constructions of new coverings of smaller size.

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عنوان ژورنال:
  • Des. Codes Cryptography

دوره 72  شماره 

صفحات  -

تاریخ انتشار 2014