Abstract

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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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 555-575
Launched on MUSE
1999-06-01
Open Access
No
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