English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Wachter-Zeh in [42], and later together with Raviv [31], proved thatGabidulin codes cannot be efficiently list decoded for any radius $\tau$,providing that $\tau$ is large enough. Also, they proved that there areinfinitely many choices of the parameters for which Gabidulin codes cannot beefficiently list decoded at all. Subsequently, in [41] these results have beenextended to the family of generalized Gabidulin codes and to further family ofMRD-codes. In this paper, we provide bounds on the list size of rank-metriccodes containing generalized Gabidulin codes in order to determine whether ornot a polynomial-time list decoding algorithm exists. We detect severalfamilies of rank-metric codes containing a generalized Gabidulin code assubcode which cannot be efficiently list decoded for any radius large enoughand families of rank-metric codes which cannot be efficiently list decoded.These results suggest that rank-metric codes which are$\mathbb{F}_{q^m}$-linear or that contains a (power of) generalized Gabidulincode cannot be efficiently list decoded for large values of the radius.

On the list decodability of rank-metric codes containing Gabidulin codes