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International Journal of Mathematics and Mathematical Sciences
Volume 2, Issue 2, Pages 261-281
http://dx.doi.org/10.1155/S0161171279000247

The (16,16,2) designs

1Department of Mathematics, Lehigh University, Bethlehem 18015, Pennsylvania, USA
2Department of Mathematics, Lafayette College, Easton 18042, Pennsylvania, USA

Received 15 November 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Elementary techniques of algebraic coding theory are here used to discuss the three biplanes with k=6. These three designs are intimately related to the (16,11) extended binary Hamming code and to one another; we systematically investigate these relationships.

We also exhibit each of the three designs as difference sets.