Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and Optimality of $w$-Non-adjacent Forms with an Algebraic
  Integer Base   We consider digital 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.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom