On the Optimality of Gauss's Algorithm over Euclidean Imaginary Quadratic Fields
Information Theory
2019-05-06 v1 math.IT
Number Theory
Abstract
In this paper, we continue our previous work on the reduction of algebraic lattices over imaginary quadratic fields for the special case when the lattice is spanned over a two dimensional basis. In particular, we show that the algebraicvariant of Gauss algorithm returns a basis that corresponds to the successive minima of the lattice in polynomial time if the chosen ring is Euclidean.
Keywords
Cite
@article{arxiv.1904.05285,
title = {On the Optimality of Gauss's Algorithm over Euclidean Imaginary Quadratic Fields},
author = {Christian Porter and Shanxiang Lyu and Cong Ling},
journal= {arXiv preprint arXiv:1904.05285},
year = {2019}
}
Comments
Conference paper in preprint, submitted to ITW 2019. arXiv admin note: text overlap with arXiv:1806.03113