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MacWilliams Extension Theorem for MDS additive codes

Abstract : The MacWilliams Extension Theorem states that each linear isometry of a linear code extends to a monomial map. Unlike the linear codes, in general, additive codes do not have the extension property. In this paper, an analogue of the extension theorem for additive codes in the case of additive MDS codes is proved. More precisely, it is shown that for almost all additive MDS codes their additive isometries extend to isometries of the ambient space. There are also described some new classes of additive codes for which an extension theorem holds.
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Submitted on : Thursday, February 18, 2016 - 10:12:41 AM
Last modification on : Tuesday, December 7, 2021 - 3:16:02 PM
Long-term archiving on: : Thursday, May 19, 2016 - 10:30:42 AM


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  • HAL Id : hal-01275761, version 1



Serhii Dyshko. MacWilliams Extension Theorem for MDS additive codes. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Apr 2015, Paris, France. ⟨hal-01275761⟩



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