  Motivated by applications in distributed storage, distributed computing, and
homomorphic secret sharing, we study communication-efficient schemes for
computing linear combinations of coded symbols. Specifically, we design
low-bandwidth schemes that evaluate the weighted sum of $\ell$ coded symbols in
a codeword $\pmb{c}\in\mathbb{F}^n$, when we are given access to $d$ of the
remaining components in $\pmb{c}$.
  Formally, suppose that $\mathbb{F}$ is a field extension of $\mathbb{B}$ of
degree $t$. Let $\pmb{c}$ be a codeword in a Reed-Solomon code of dimension $k$
and our task is to compute the weighted sum of $\ell$ coded symbols. In this
paper, for some $s<t$, we provide an explicit scheme that performs this task by
downloading $d(t-s)$ sub-symbols in $\mathbb{B}$ from $d$ available nodes,
whenever $d\geq \ell|\mathbb{B}|^s-\ell+k$. In many cases, our scheme
outperforms previous schemes in the literature.
  Furthermore, we provide a characterization of evaluation schemes for general
linear codes. Then in the special case of Reed-Solomon codes, we use this
characterization to derive a lower bound for the evaluation bandwidth.
