  In this paper, we study algebraic geometry codes from curves over
$\mathbb{F}_{q^\ell}$ through their virtual projections which are algebraic
geometric codes over $\mathbb{F}_q$. We use the virtual projections to provide
fractional decoding algorithms for the codes over $\mathbb{F}_{q^\ell}$.
Fractional decoding seeks to perform error correction using a smaller fraction
of $\mathbb{F}_q$-symbols than a typical decoding algorithm. In one instance,
the bound on the number of correctable errors differs from the usual lower
bound by the degree of a pole divisor of an annihilator function. In another,
we view the virtual projections as interleaved codes to, with high probability,
correct more errors than anticipated.
