Blar i forfatter "Shiromoto, Keisuke"

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    • A generalization of Kung’s theorem 

      Johnsen, Trygve; Shiromoto, Keisuke; Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed, 2015-10-01)
      We give a generalization of Kung’s theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all i=k+1,…,ni=k+1,…,n, we give an upper bound on the smallest integer m such that there exist m codewords whose union of supports has cardinality at least i.

    • Wei-type duality theorems for matroids 

      Britz, Thomas; Johnsen, Trygve; Mayhew, Dillon; Shiromoto, Keisuke (Journal article; Tidsskriftartikkel; Peer reviewed, 2012)
      We present several fundamental duality theorems for matroids and more general combinatorial structures. As a special case, these results show that the maximal cardinalities of fixed-ranked sets of a matroid determine the corresponding maximal cardinalities of the dual matroid. Our main results are applied to perfect matroid designs, graphs, transversals, and linear codes over division rings, in each ...