Details

Autor(en) / Beteiligte

• Bonini, Matteo
• Borello, Martino

Titel

Minimal linear codes arising from blocking sets

Ist Teil von

• Journal of algebraic combinatorics, 2021-03, Vol.53 (2), p.327-341

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2021

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Minimal linear codes are algebraic objects which gained interest in the last 20 years, due to their link with Massey’s secret sharing schemes. In this context, Ashikhmin and Barg provided a useful and a quite easy-to-handle sufficient condition for a linear code to be minimal, which has been applied in the construction of many minimal linear codes. In this paper, we generalize some recent constructions of minimal linear codes which are not based on Ashikhmin–Barg’s condition. More combinatorial and geometric methods are involved in our proofs. In particular, we present a family of codes arising from particular blocking sets, which are well-studied combinatorial objects. In this context, we will need to define cutting blocking sets and to prove some of their relations with other notions in blocking sets’ theory. At the end of the paper, we provide one explicit family of cutting blocking sets and related minimal linear codes, showing that infinitely many of its members do not satisfy the Ashikhmin–Barg’s condition.