منابع مشابه
Cycle Structures of Orthomorphisms Extending Partial Orthomorphisms of Boolean Groups
A partial orthomorphism of a group G (with additive notation) is an injection π : S → G for some S ⊆ G such that π(x) − x 6= π(y) − y for all distinct x, y ∈ S. We refer to |S| as the size of π, and if S = G, then π is an orthomorphism. Despite receiving a fair amount of attention in the research literature, many basic questions remain concerning the number of orthomorphisms of a given group, a...
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Linear orthomorphism has the well diffusibility, which can be used to design P-permutation in cryptography. This paper presents the definition of the linear orthomorphisms and orthomorphic matrices on the integer residue class ring, whose counting formulas have been obtained too. They have provided a theoretical basis to research the nature of orthomorphisms on the ring in the cryptography.
متن کاملAtomic Latin Squares based on Cyclotomic Orthomorphisms
Atomic latin squares have indivisible structure which mimics that of the cyclic groups of prime order. They are related to perfect 1-factorisations of complete bipartite graphs. Only one example of an atomic latin square of a composite order (namely 27) was previously known. We show that this one example can be generated by an established method of constructing latin squares using cyclotomic or...
متن کاملOrthomorphisms and the construction of projective planes
We discuss a simple computational method for the construction of finite projective planes. The planes so constructed all possess a special group of automorphisms which we call the group of translations, but they are not always translation planes. Of the four planes of order 9, three admit the additive group of the field GF (9) as a group of translations, and the present construction yields all ...
متن کاملCyclotomic R-orthomorphisms of finite fields
A polynomial f (X) over a finite field is an orthomorphism if both f (X) and f (X) − X are permutation polynomials. We prove the existence of several classes of cyclotomic orthomorphisms and extend the results toR-orthomorphisms. © 2005 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1975
ISSN: 0021-9045
DOI: 10.1016/0021-9045(75)90052-0