  Let $b$ be an algebraic number with $|b|>1$ and $\mathcal{H}$ a finite set of
algebraic numbers. We study the transcendence of numbers of the form
$\sum_{n=0}^\infty \frac{a_n}{b^n}$ where $a_n \in \mathcal{H}$ for all
$n\in\mathbb{N}$. We assume that the sequence $(a_n)_{n=0}^\infty$ is generated
by coding the orbit of a point under an irrational rotation of the unit circle.
In particular, this assumption holds whenever the sequence is Sturmian. Our
main result shows that all numbers of the above form are transcendental. We
moreover give sufficient conditions for a finite set of such numbers to be
linearly independent over~$\bar{\mathbb{Q}}$.
