  In this work, we present linear exact repair schemes for one or two erasures
in decreasing monomial-Cartesian codes DM-CC, a family of codes which provides
a framework for polar codes. In the case of two erasures, the positions of the
erasures should satisfy a certain restriction. We present families of augmented
Reed-Muller (ARM) and augmented Cartesian codes (ACar) which are families of
evaluation codes obtained by strategically adding vectors to Reed-Muller and
Cartesian codes, respectively. We develop repair schemes for one or two
erasures for these families of augmented codes. Unlike the repair scheme for
two erasures of DM-CC, the repair scheme for two erasures for the augmented
codes has no restrictions on the positions of the erasures. When the dimension
and base field are fixed, we give examples where ARM and ACar codes provide a
lower bandwidth (resp., bitwidth) in comparison with Reed-Solomon (resp.,
Hermitian) codes. When the length and base field are fixed, we give examples
where ACar codes provide a lower bandwidth in comparison with ARM. Finally, we
analyze the asymptotic behavior when the augmented codes achieve the maximum
rate.
