Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal weight expansions in Pisot bases   For applications to cryptography, it is important to represent numbers with a
small number of non-zero digits (Hamming weight) or with small absolute sum of
digits. The problem of finding representations with minimal weight has been
solved for integer bases, e.g. by the non-adjacent form in base~2. In this
paper, we consider numeration systems with respect to real bases $\beta$ which
are Pisot numbers and prove that the expansions with minimal absolute sum of
digits are recognizable by finite automata. When $\beta$ is the Golden Ratio,
the Tribonacci number or the smallest Pisot number, we determine expansions
with minimal number of digits $\pm1$ and give explicitely the finite automata
recognizing all these expansions. The average weight is lower than for the
non-adjacent form.

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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th