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.

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ABSTRACT. The four known biplanes of order 9 (k ii) are described in terms of their ovals, %-chain structures, and automorphism groups. An exhaustive computer search for all biplanes of order 9 with certain chain structures has produced but two, one of which is new. None of these four biplanes yield the putative plane of order i0.