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

Coding with Constraints: Minimum Distance Bounds and Systematic Constructions