Existence and Optimality of $w$-Non-adjacent Forms with an Algebraic Integer Base
Number Theory
2015-04-13 v1
Abstract
We consider digital expansions in lattices with endomorphisms acting as base. We focus on the -non-adjacent form (-NAF), where each block of consecutive digits contains at most one non-zero digit. We prove that for sufficiently large and an expanding endomorphism, there is a suitable digit set such that each lattice element has an expansion as a -NAF. If the eigenvalues of the endomorphism are large enough and is sufficiently large, then the -NAF is shown to minimise the weight among all possible expansions of the same lattice element using the same digit system.
Cite
@article{arxiv.1205.4414,
title = {Existence and Optimality of $w$-Non-adjacent Forms with an Algebraic Integer Base},
author = {Clemens Heuberger and Daniel Krenn},
journal= {arXiv preprint arXiv:1205.4414},
year = {2015}
}