Computing Linear Codes and Unitals

Authors:
David B. Jaffe;Vladimir D. Tonchev
Affiliations:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588-0323, USA. E-mail: djaffe@math.mtu.edu;Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931, USA. E-mail tonchev@math.mtu.edu
Venue:
Designs, Codes and Cryptography
Year:
1998

Citing 7
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Abstract

The 2-rank of any 2-(28,4,1) design (unital on 28 points)is known to be between 19 and 27. It is shown by the enumerationand analysis of certain binary linear codes that there are nounitals of 2-rank 20, and that there are exactly 4 isomorphismclasses of unitals of 2-rank 21. Combined with previous results,this completes the classification of unitals on 28 points of2-rank less than 22.