  We examine an error-correcting coding framework in which each coded symbol is
constrained to be a function of a fixed subset of the message symbols. With an
eye toward distributed storage applications, we seek to design systematic codes
with good minimum distance that can be decoded efficiently. On this note, we
provide theoretical bounds on the minimum distance of such a code based on the
coded symbol constraints. We refine these bounds in the case where we demand a
systematic linear code. Finally, we provide conditions under which each of
these bounds can be achieved by choosing our code to be a subcode of a
Reed-Solomon code, allowing for efficient decoding. This problem has been
considered in multisource multicast network error correction. The problem setup
is also reminiscent of locally repairable codes.
