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Counting problems for orthogonal sets and sublattices in function fields
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DOI：10.1112/mtk.70083.png)
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Abstract
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Let . Analogous to orthogonality in the Euclidean space , there exists a well-studied notion of ultrametric orthogonality in . In this paper, we extend the work of [4] on counting problems related to orthogonality in . For example, we resolve an open question posed in [4] by bounding the size of the largest orthogonal sets in . Furthermore, using similar ideas and techniques, we investigate analogues of Hadamard matrices over . Finally, we also use ultrametric orthogonality to compute the number of sublattices of with a certain geometric structure, and to determine the number of orthogonal bases of a sublattice in . The resulting formulas depend crucially on successive minima.
Keywords:
VECTORS
GEOMETRY
NUMBERS
(T
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