The nonexistence of \([51,5,33;3]\)-codes

Noboru Hamada1, Tor Helleseth2, Oyvind Ytrehus2
1Department of Applied Mathematics, Osaka Women’s University, Sakai, Osaka, Japan 590.
2Department of Infor- matics, University of Bergen, Thormghlensgt. 55, N-S008 Bergen, Norway.

Abstract

It is unknown whether or not there exists a \([51, 5, 33; 3]\)-code (meeting the Griesmer bound). The purpose of this paper is to show that there is no \([51, 5, 33; 3]\)-code.