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General methods from  are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.
319 Corollary 4.3: For each possible value , there exists a unique additive dual code H of the extended 1-perfect additive non-4-linear code and all these codes H are pairwise nonequivalent, except for = 0 and = 1, where the codes H coincide with the binary dual of the extended Hamming code. ACKNOWLEDGMENT The authors would like to thank the anonymous… (More)
In the vein of Christol, Kamae, Mendès France and Rauzy, we consider the analogue of a problem of Mahler for rational functions in positive characteristic. To solve this question, we prove an extension of Cobham's theorem for quasi-automatic functions and use the recent generalization of Christol's theorem obtained by Kedlaya.
Many classical results concerning quadratic forms have been extended to hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cancellation result, an analogue of Springer's theorem, as well as some local-global and finiteness results… (More)
Let k be a field of characteristic = 2, and let L be a Galois extension of k with group G. Let us denote by q L : L × L → k the trace form, defined by q L (x, y) = Tr L/k (xy). Let (gx) g∈G be a normal basis of L over k. We say that this is a self–dual normal basis if q L (gx, hx) = δ g,h. If the order of G is odd, then L always has a self–dual normal basis… (More)
The meeting focussed on lattices and their applications in mathematics and information technology. The research interests of the participants varied from engineering sciences, algebraic and analytic number theory, coding theory, algebraic geometry to name only a few.
— In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a neg-ligeable coding gain. Lattice constellations with high… (More)