Abstract
The polynomial formulation of generalized ReedMuller codes, first introduced by Kasami, Lin, and Peterson is somewhat formalized and an extensive study is made of the interrelations between the m -variable approach of Kasami, Lin, and Peterson and the one-variable approach of Mattson and Solomon. The automorphism group is studied in great detail, both in the m -variable and in the one-variable language. The number of minimum weight vectors is obtained in the general case. Two ways of restricting generalized ReedMuller codes to subcodes are studied: the nonprimitive and the subfield subcodes. Connections with geometric codes are pointed out and a new series of majority decodable codes is introduced.
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