On Generalized Reed-Muller Codes and Their Relatives

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.

• Publication year

  1970

• Venue

  Information and Control

• Publication date

  1970-07-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/S0019-9958(70)90214-7
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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