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The ubiquity of order domains for the construction of error control codes
2007
Advances in Mathematics of Communications
The order domains are a class of commutative rings introduced by Høholdt, van Lint, and Pellikaan to simplify the theory of error control codes using ideas from algebraic geometry. The definition is largely motivated by the structures utilized in the Berlekamp-Massey-Sakata (BMS) decoding algorithm, with Feng-Rao majority voting for unknown syndromes, applied to one-point geometric Goppa codes constructed from curves. However, order domains are much more general, and O'Sullivan has shown that
doi:10.3934/amc.2007.1.151
fatcat:62gcwxj7zrce7e7fshtvtozqyi