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By A. Barlotti, M. Biliotti, A. Cossu, G. Korchmaros and G. Tallini (Eds.)

ISBN-10: 0444879625

ISBN-13: 9780444879622

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Additional info for Combinatorics ’84, Proceedings of the International Conference on Finite Geometries and Combinatorial Structures

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Mat. F i s . M o d e n a 31 ( 1 9 8 3 ) 1 3 0 - 1 5 7 . , P a r t i a l s p r e a d s i n f i n i t e p r o j e c t i v e s p a c e s a n d p a r t i a l d e s i g n s , M a t h . 2. 145 ( 1 9 7 5 ) 2 1 1 - 2 3 0 . ,Blocking sets and p a r t i a l spreads i n finite p r o j e c t i v e s p a c e s , Geom. D e d i c a t a 9 ( 1 9 8 0 ) 4 2 5 - 4 4 9 . C.. A characterization of flat spaces i n a f i n i t e g e o m e t r y a n d t h e u n i q u e n e s s o f t h e Hamming a n d the Mac D o n a l d c o d e s , J .

Fix a line H of S , and let a, c, d, e and x be integers with the following properties: (1) The degree of H is n+l-d < n+l. (2) The number of lines parallel to H is nd+x > 0. ( 3 ) For every parallel L of H we have n+a 5 h(L,H) 5 n+c. ( 4 ) For any two intersecting lines Llf L2 parallel to H we have h(L1,L2) 5 e. (5) 2n > (d+l)(de-d-2a-2) + 2x. (6) n > (2d-l)(c+l) + e - 1 - 2x. (7) At least one of the following assertions is true: (i) On every parallel of H there is a point of degree n+l, or (ii) n(d-s) > s(c+l) - x for every integer s with 0 5 s 5 d-1.

N) the equivalence classes contain exactly X points. Let H := {hi, hrl be a block of T(t,AP-l,r,n) and let x be an arbitrary point. Put Xi :=hw iff x,hV are in the same column of Mi. ,xn) does not determine the point x. But there are X points equivalent to x. We xn,u), u = 1 , A We construct the permutation call them (XI, sets r 2 , rn the same way it was done in the proof of Theorem 5. To every block ... , . ,X}: Put Cp(i) = v p in case xpl = hi. Call 4(t,X,r) the set of it all such functions stemming from blocks.

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Combinatorics ’84, Proceedings of the International Conference on Finite Geometries and Combinatorial Structures by A. Barlotti, M. Biliotti, A. Cossu, G. Korchmaros and G. Tallini (Eds.)


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