Abstract. XTR is a general method that can be applied to discrete logarithm based cryptosystems in extension fields of degree six, providing a compact representation of the elements involved. In this paper we present a precise formulation of the Brouwer-Pellikaan-Verheul conjecture, originally posed in [4], concerning the size of XTR-like representations of elements in extension fields of arbitrary degree. If true this conjecture would provide even more compact representations of elements than XTR in extension fields of degree thirty. We test the conjecture by experiment, showing that in fact it is unlikely that such a compact representation of elements can be achieved in extension fields of degree thirty.
Since reading the paper upon the theory of the earth, I have been employed in examining many parts of this country, in order to enquire into the natural history of granite. In this undertaking, I have succeeded beyond my most flattering expectations; and I am now to communicate to this Society the result of my observations.In the paper just referred to, it was maintained, from many different arguments, that all the solid strata of the earth had been consolidated by means of subterraneous heat, softening the hard materials of those bodies; and that in many places, those consolidated strata had been broken and invaded by huge masses of fluid matter similar to lava, but, for the most part, perfectly distinguishable from it. Granite also was considered there as a body which had been certainly consolidated by heat; and which had, at least in some parts, been in the state of perfect fusion, and certain specimens were produced, from which I drew an argument in support of this conclusion.
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