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Problemy Peredachi Informatsii, 1998, Volume 34, Issue 3, Pages 50–59 (Mi ppi417)  
Coding Theory

Pairing of Finite Modules, Duality of Linear Codes, and the MacWilliams Identities

O. A. Logachev, A. A. Sal'nikov, V. V. Yashchenko
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Abstract: The concept of the duality of codes well known in coding theory is introduced for submodules of a pair of finite modules related by a ertain binary bilinear relation. Therewith, a air of antiisomorphic complete lattices of dual submodules arises. Under certain conditions, the MacWilliams identities which connect the characteristics of a pair of mutually dual codes are proved.
Received: 28.04.1997
Revised: 12.03.1998
Bibliographic databases:
Document Type: Article
UDC: 621.391.15
Language: Russian
Citation: O. A. Logachev, A. A. Sal'nikov, V. V. Yashchenko, “Pairing of Finite Modules, Duality of Linear Codes, and the MacWilliams Identities”, Probl. Peredachi Inf., 34:3 (1998), 50–59; Problems Inform. Transmission, 34:3 (1998), 250–258
Citation in format AMSBIB
\Bibitem{LogSalYas98}
\by O.~A.~Logachev, A.~A.~Sal'nikov, V.~V.~Yashchenko
\paper Pairing of Finite Modules, Duality of Linear Codes, and the MacWilliams Identities
\jour Probl. Peredachi Inf.
\yr 1998
\vol 34
\issue 3
\pages 50--59
\mathnet{http://mi.mathnet.ru/ppi417}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1663926}
\zmath{https://zbmath.org/?q=an:0990.94029}
\transl
\jour Problems Inform. Transmission
\yr 1998
\vol 34
\issue 3
\pages 250--258
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    		Проблемы передачи информации Problems of Information Transmission
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