Duality for modules over finite rings and applications to coding theory | Zendy

Jay A. Wood | Zendy

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Duality for modules over finite rings and applications to coding theory

Author(s) -

Jay A. Wood

Publication year - 1999

Publication title -

american journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.818

H-Index - 67

eISSN - 1080-6377

pISSN - 0002-9327

DOI - 10.1353/ajm.1999.0024

Subject(s) - mathematics , duality (order theory) , finite field , ring (chemistry) , pure mathematics , coding (social sciences) , coding theory , discrete mathematics , algebra over a field , chemistry , statistics , organic chemistry

This paper sets a foundation for the study of linear codes over finite rings. The finite Frobenius rings are singled out as the most appropriate for coding theoretic purposes because two classical theorems of MacWilliams, the extension theorem and the MacWilliams identities, generalize from finite fields to finite Frobenius rings. It is over Frobenius rings that certain key identifications can be made between the ring and its complex characters.

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