The Hermite normal form for certain rank-1 circulant and skew-circulant lattice rules
Joe, S. (2016). The Hermite normal form for certain rank-1 circulant and skew-circulant lattice rules. Linear Algebra and Its Applications, 496, 438–451. https://doi.org/10.1016/j.laa.2016.02.009
Permanent Research Commons link: https://hdl.handle.net/10289/11168
Characterisations are provided of the Hermite normal form of certain integer circulant and skew-circulant matrices. These matrices are associated with rank-1 circulant and skew-circulant lattice rules. Previous computer searches for lattice rules of specified trigonometric degree have indicated that there is some merit in searches of such lattice rules. We also consider the question of whether a Hermite normal form with the characterisation for these rank-1 circulant lattice rules is actually associated to a circulant lattice rule. Though the answer is negative in the general case, several examples where the answer is positive will be given.
This is an author’s accepted version of an article published in the journal: Linear Algebra and its Applications. © 2016 Elsevier.