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By Fiske T.S.

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The reader can verify that this is a representation; it is enough to show that the matrices M. satisfy the same recursion as the polynomials 0i(A). ) It follows that Mj=0j(M1), 0:5 jsm, and if N. is the matrix representing Ej(0), then j(M1), 0

We are given some kind of geometrical 'system', and are also given a particularly pleasant system S0 of this kind which has no proper subsystems except for trivial ones; we want to find all those systems S with the property that all their 'minimally generated' non-trivial subsystems are isomorphic to So. Theorem 2. 1 answers this question for parallelX is ms of (t) in the case where S0 is the parallelism with n = 2t. (For other theorems of this type, see the Veblen-Young axiomatization of projective geometries [VY], and also Buekenhout [6], Hall [14], Young [37], and Gleason's theorem in Dembowski [D], p.

Theorem 3A. 15. S(4, 7, 23) is unique (up to isomorphism). Proof. If S' is such a system and Sp = S', we can identify S with the system in the last theorem in such a way that the points p correspond. // The perfect 3-error-correcting linear binary code of length 23 is unique (up to isomorphism). // Theorem 3A. 16.

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Functions of a complex variable by Fiske T.S.


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