Strongly Reduced Lattice Bases. (arXiv:2304.12135v2 [math.NT] UPDATED)

In this paper, we show that for each lattice basis, there exists an
equivalent basis which we describe as ``strongly reduced''. We show that bases
reduced in this manner exhibit rather ``short'' basis vectors, that is, the
length of the $i$th basis vector of a strongly reduced basis is upper bounded
by a polynomial factor in $i$ multiplied by the $i$th successive minima of the
lattice. The polynomial factor seems to be smaller than other known factors in
literature, such …

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