English

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

R2 v1 2026-06-23T08:35:39.538Z