Full Characterization of Minimal Linear Codes as Cutting Blocking Sets release_dxz7c4abtnfpnktjv75xnki6j4

by Chunming Tang, Yan Qiu, Qunying Liao, Zhengchun Zhou

Released as a article .

2019  

Abstract

In this paper, we first study more in detail the relationship between minimal linear codes and cutting blocking sets, which were recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking sets. As a direct result, minimal projective codes of dimension 3 and t-fold blocking sets with t> 2 in projective planes are identical objects. Some bounds on the parameters of minimal codes are derived from this characterization. Using this new link between minimal codes and blocking sets, we also present new general primary and secondary constructions of minimal linear codes. Resultantly, infinite families of minimal linear codes not satisfying the Aschikhmin-Barg's condition are obtained. In addition, the weight distributions of two subfamilies of the proposed minimal linear codes are established. Open problems are also presented.
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Date   2019-11-22
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arXiv  1911.09867v1
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