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Algebraic Coding and Cryptography
Online Event
ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
ACCESS is a joint effort designed to highlight world-class research in coding theory, cryptography, and related areas and to encourage collaboration among its participants.
Next seminar
May 06
Next seminar
May 06
Trygve Johnson
The Arctic University of Norway
Trygve Johnson
The Arctic University of Norway
Vector rank metric codes, and associated combinatorial structures
Vector rank metric codes, and associated combinatorial structures
Abstract. We will treat some similarities and differences between ”usual” linear codes with Hamming metric, and vector rank metric codes. We will study matroids and q-matroids associated to these codes, and we will show how certain complexes associated to these combinatorial structures are less easily applied for vector codes with the rank metric (leading to q-matroids) than for codes with the Hamming metric (leading to matroids). We will mention how one (at least in part) can overcome this problem for vector rank metric codes, for example by reducing to a study of associated (usual, not q-)matroids.
Biography. Trygve Johnsen received the cand.real (M.Sc.) and Dr.Sci.(Ph.D.) degrees from the University of Oslo, Norway, in 1981 and 1984, respectively, both in mathematics. In 1982-1987 he was affiliated to the Department of Mathematics at the University of Oslo, and in 1987-1994 he was at the University of Tromsø, Norway. In 1995-2007 he was with the Department of Mathematics at the University of Bergen, Norway, and since 2008 he is once again with the University of Tromsø (Department of Mathematics and Statistics). Most of his early research was within algebraic geometry, but during the last 15 years most of his research has been within the fields of error-correcting codes, matroid theory, and related objects.
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