Can I read MacWilliams' Extension Theorem for rank-metric codes on EtoBox?

MacWilliams' Extension Theorem for rank-metric codes by Gorla, Elisa; Salizzoni, Flavio is a scholarly article available to read on EtoBox.

What is MacWilliams' Extension Theorem for rank-metric codes about?

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.

Author

Gorla, Elisa; Salizzoni, Flavio

Published

2023

Language

EN