97 research outputs found
Left-ordered inp-minimal groups
We prove that any left-ordered inp-minimal group is abelian, and we provide
an example of a non-abelian left-ordered group of dp-rank 2
p-Adic valuation of weights in Abelian codes over /spl Zopf/(p/sup d/)
Counting polynomial techniques introduced by Wilson are used to provide analogs of a theorem of McEliece. McEliece's original theorem relates the greatest power of p dividing the Hamming weights of words in cyclic codes over GF (p) to the length of the smallest unity-product sequence of nonzeroes of the code. Calderbank, Li, and Poonen presented analogs for cyclic codes over /spl Zopf/(2/sup d/) using various weight functions (Hamming, Lee, and Euclidean weight as well as count of occurrences of a particular symbol). Some of these results were strengthened by Wilson, who also considered the alphabet /spl Zopf/(p/sup d/) for p an arbitrary prime. These previous results, new strengthened versions, and generalizations are proved here in a unified and comprehensive fashion for the larger class of Abelian codes over /spl Zopf/(p/sup d/) with p any prime. For Abelian codes over /spl Zopf//sub 4/, combinatorial methods for use with counting polynomials are developed. These show that the analogs of McEliece's theorem obtained by Wilson (for Hamming weight, Lee weight, and symbol counts) and the analog obtained here for Euclidean weight are sharp in the sense that they give the maximum power of 2 that divides the weights of all the codewords whose Fourier transforms have a specified support
Panorama of p-adic model theory
ABSTRACT. We survey the literature in the model theory of p-adic numbers since\ud
Denefâs work on the rationality of PoincarĂ© series. / RĂSUMĂ. Nous donnons un aperçu des dĂ©veloppements de la thĂ©orie des modĂšles\ud
des nombres p-adiques depuis les travaux de Denef sur la rationalité de séries de Poincaré,\ud
par une revue de la bibliographie
An example of a -minimal structure without definable Skolem functions
We show there are intermediate -minimal structures between the
semi-algebraic and sub-analytic languages which do not have definable Skolem
functions. As a consequence, by a result of Mourgues, this shows there are
-minimal structures which do not admit classical cell decomposition.Comment: 9 pages, (added missing grant acknowledgement
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