1. MacWilliams' Extension Theorem for rank-metric codes.
- Author
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Gorla, Elisa and Salizzoni, Flavio
- Subjects
- *
HAMMING distance - Abstract
The MacWilliams' Extension Theorem is a classical result by Florence Jessie MacWilliams. It shows that every linear isometry between linear block-codes endowed with the Hamming distance can be extended to a linear isometry of the ambient space. Such an extension fails to exist in general for rank-metric codes, that is, one can easily find examples of linear isometries between rank-metric codes which cannot be extended to linear isometries of the ambient space. In this paper, we explore to what extent a MacWilliams' Extension Theorem may hold for rank-metric codes. We provide an extensive list of examples of obstructions to the existence of an extension, as well as a positive result. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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