Recent advances on minimal codes

Abstract

In this short survey we concern ourselves with minimal codes, a classical object in coding theory. We will explain the relation between minimal codes and various other mathematical domains, in particular with finite projective geometry. This latter connection has sparked a renewed interest in minimal codes, giving rise to new constructions as well as new questions.

Theorems & Definitions (27)

• Definition 2.1
• Definition 2.2
• Definition 2.3
• Proposition 3.1: chabanne2013towards, Theorem 2.
• Proposition 3.2: ashikhmin1998minimal, Lemma 2.1. (2.)
• Theorem 3.3: ashikhmin1998minimal, Lemma 2.1. (3.)
• Theorem 3.4: ABNgeo, Theorem 3.4., tang2019full, Theorem 14.
• Proposition 3.5: ABNgeo, Theorem 4.3.
• Proposition 3.6: 3CB, Theorem 2.8.
• Theorem 3.7: 3CB, Theorem 2.14.