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Binary additive MRD codes with minimum distance n-1 must contain a semifield spread set
John Sheekey
In this paper we prove a result on the structure of the elements of an additive {\it maximum rank distance (MRD) code} over the field of order two, namely that in some cases such c…
Rank-metric codes, linear sets, and their duality
John Sheekey, Geertrui Van de Voorde
In this paper we investigate connections between linear sets and subspaces of linear maps. We give a geometric interpretation of the results of [18, Section 5] on linear sets on a…
A Characterization of the Number of Roots of Linearized and Projective Polynomials in the Field of Coefficients
Gary McGuire, John Sheekey
A fundamental problem in the theory of linearized and projective polynomials over finite fields is to characterize the number of roots in the coefficient field directly from the co…
New Semifields and new MRD Codes from Skew Polynomial Rings
John Sheekey
In this article we construct a new family of semifields, containing and extending two well-known families, namely Albert's generalised twisted fields and Petit's cyclic semifields…