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math.NT2022
A New Bound for the Orthogonality Defect of HKZ Reduced Lattices
Christian Porter, Edmund Dable-Heath, Cong Ling
In this work, we determine a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension . Using this result, we determine a general upper bound for the o…
math.NT2021
Reduction Theory of Algebraic Modules and their Successive Minima
Christian Porter, Cong Ling
Lattices defined as modules over algebraic rings or orders have garnered interest recently, particularly in the fields of cryptography and coding theory. Whilst there exist many at…