FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1227-1236

Extension theorem for linear codes over finite quasi-Frobenius modules

I. L. Kheifets

Abstract

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F. J. MacWilliams proved an Extension theorem: Hamming isometries between linear codes over finite fields extend to monomial transformation. This result has been generalized by J. A. Wood who proved it for Frobenius rings. In this paper the Extension theorem for linear codes over a finite quasi-Frobenius module with commutative coefficient ring is proved. The main technique involves the description of quasi-Frobenius module in terms of character theory.

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