منابع مشابه
On projective planes of order less than 32
By our count, 245 projective planes of order less than 32 are currently known. This list is dominated by the 193 known planes of order 25. Most of these are either translation planes or Hughes planes, or planes obtained from these by the well-known process of repeatedly dualizing and deriving. We describe two new planes obtainable by the quite different method of ‘lifting quotients’. 2000 Mathe...
متن کاملTernary dual codes of the planes of order nine
We determine the minimum weight of the ternary dual codes of each of the four projective planes of order 9, and of the seven affine planes of order 9. The proof includes a construction of a word of small, sometimes minimal, weight in the dual code of any plane of square order containing a Baer subplane. Dedicated to S. S. Shrikhande
متن کاملGroups of generalised projectivities in projective planes of odd order
The generalised projectivities (GP's) associated with projective planes of odd order are investigated. These are non-singular linear mappings over GF(2) defined from the binary codes of these planes. One case that is investigated in detail corresponds to the group of an affine plane-every point corresponds to a GP. It is shown how many collineations that fix the line at infinity point-wise can ...
متن کاملGraphs for Orthogonal Arrays and Projective Planes of Even Order
We consider orthogonal arrays of strength two and even order q having n columns which are equivalent to n − 2 mutually orthogonal Latin squares of order q. We show that such structures induce graphs on n vertices, invariant up to complementation. Previous methods worked only for single Latin squares of even order and were harder to apply. If q is divisible by four the invariant graph is simple ...
متن کاملUnbalanced Hadamard Matrices and Finite Projective Planes of Even Order
By an unbalanced Hadamard matrix we mean a matrix H,, = (hii) such that (i) hii = l/fi or -I/fi, (ii) H, is orthogonal, and (iii) the number of positive entries exceeds the number of negative entries in each row. In particular it is well-known that the dimension n must be an even perfect square if the number of positive entries is the same in each row. It is easy to show that the number of posi...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1959
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1959-0107208-8