On the MacWilliams identities for linear codes
نویسندگان
چکیده
منابع مشابه
The equivalent identities of the MacWilliams identity for linear codes
Abstract We use derivatives to prove the equivalences between MacWilliams identity and its four equivalent forms, and present new interpretations for the four equivalent forms. Our results explicitly give out the relationships between MacWilliams identity and its four equivalent forms.
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Codes over various metrics such as Rosenbloom-Tsfasman (RT), Lee, etc. have been considered. Recently, codes over poset metrics have been studied. Poset metric is a great generalization of many metrics especially the well-known ones such as the RT and the Hamming metrics. Poset metric can be realized on the channels with localized error occurrences. It has been shown that MacWilliams identities...
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Abstract Motivated by the works of Shiromoto [3] and Shi et al. [4], we study the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over Zl. Necessary and sufficient conditions for the existence of MacWilliams type identities with respect to Lee and Euclidean weight enumerators for linear codes over Zl are given. Some examples about s...
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Linear codes are considered over the ring Z 4 + uZ 4 , a non-chain extension of Z 4. Lee weights, Gray maps for these codes are defined and MacWilliams identities for the complete, symmetrized and Lee weight enumer-ators are proved. Two projections from Z 4 + uZ 4 to the rings Z 4 and F 2 + uF 2 are considered and self-dual codes over Z 4 +uZ 4 are studied in connection with these projections. ...
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A partition of a finite abelian group gives rise to a dual partition on the character group via the Fourier transform. Properties of the dual partitions are investigated and a convenient test is given for the case that the bidual partition coincides the primal partition. Such partitions permit MacWilliams identities for the partition enumerators of additive codes. It is shown that dualization c...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1988
ISSN: 0024-3795
DOI: 10.1016/0024-3795(88)90244-3