SIAM Journal on Discrete Mathematics
This paper shows how to construct analogs of Reed-Muller codes from partially ordered sets. In the case that the partially ordered set is Eulerian the length of the code is the number of elements in the poset, the dimension is the size of a selected order ideal and the minimum distance is the minimum size of a principal dual ideal generated by a member of the order ideal. In this case, the majority logic method of decoding Reed-Muller codes works for incidence codes. A number of interesting combinatorial questions arise from the study of these codes.
Bogart, Kenneth P., "Incidence Codes of Posets: Eulerian Posets and Reed-Muller Codes" (1980). Open Dartmouth: Faculty Open Access Articles. 2857.