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Incidence codes of posets: Eulerian posets and Reed-Muller codes

✍ Scribed by Kenneth P. Bogart

Publisher: Elsevier Science
Year: 1980
Tongue: English
Weight: 713 KB
Volume: 31
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90167-3

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✦ Synopsis

This paper shows how to construct analogs of Reed-Muller codes from partially ordered sets. In the case that the partial:; ordered set is Eulertan the length of the code is the number of elements in the poset, the dimension is the size of a sePected 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 maiority logic method of decoding Reed-Muller codes works for incidence codes. A number of interesting combinatorial questions arise from the study of these codes.

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