Abstract
The MacWilliams identity relating the weight enumerators of a binary linear code and its dual code is generalized to linear codes over Galois rings.
Index terms — Galois ring, linear code, MacWilliams identity.
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References
M. Klemm, “Über die Identität von MacWilliams für die Gewichtsfunktion von Codes”, Arch. Math., 49, 1987, 400–406.
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North Holland, 1977.
A. A. Nechaev, “Kerdock-code in a cyclic form”, Diskretnaya Mat. (USSR), 1, 1989, 123–139 (in Russian), English translation: Discrete Math. Appl., 1, 1991, 365–384.
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© 2000 Springer Science+Business Media New York
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Wan, ZX. (2000). The MacWilliams Identity for Linear Codes over Galois Rings. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_27
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DOI: https://doi.org/10.1007/978-1-4757-6048-4_27
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4967-7
Online ISBN: 978-1-4757-6048-4
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