We consider digit expansions in lattices with endomorphisms acting as base. We focus on the w-non-adjacent form (w-NAF), where each block of w consecutive digits contains at most one non-zero digit. We prove that for sufficiently large w and an expanding endomorphism, there is a suitable digit set such that each lattice element has an expansion as a w-NAF. If the eigenvalues of the endomorphism are large enough and w is sufficiently large, then the w-NAF is shown to minimise the weight among all possible expansions of the same lattice element using the same digit system. © 2013 Akadémiai Kiadó, Budapest, Hungary.
CITATION STYLE
Heuberger, C., & Krenn, D. (2013). Existence and optimality of w-non-adjacent forms with an algebraic integer base. Acta Mathematica Hungarica, 140(1–2), 90–104. https://doi.org/10.1007/s10474-013-0303-2
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