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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we first study in detail the relationship between minimallinear codes and cutting blocking sets, which were recently introduced byBonini and Borello, and then completely characterize minimal linear codes ascutting blocking sets. As a direct result, minimal projective codes ofdimension $3$ and $t$-fold blocking sets with $t\ge 2$ in projective planes areidentical objects. Some bounds on the parameters of minimal codes are derivedfrom this characterization. This confirms a recent conjecture by Alfarano,Borello and Neri in [a geometric characterization of minimal codes and theirasymptotic performance, arXiv:1911.11738, 2019] about a lower bound of theminimum distance of a minimal code. Using this new link between minimal codesand blocking sets, we also present new general primary and secondaryconstructions of minimal linear codes. As a result, infinite families ofminimal linear codes not satisfying the Aschikhmin-Barg's condition areobtained. In addition to this, the weight distributions of two subfamilies ofthe proposed minimal linear codes are established. Open problems are alsopresented.

Full Characterization of Minimal Linear Codes as Cutting Blocking Sets