Geometric dual and sum‐rank minimal codes - CNRS - Centre national de la recherche scientifique
Journal Articles Journal of Combinatorial Designs Year : 2024

Geometric dual and sum‐rank minimal codes

Ferdinando Zullo

Abstract

Abstract The main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum‐rank metric. These objects form a bridge between the classical minimal codes in the Hamming metric, the subject of intense research over the past three decades partly because of their cryptographic properties, and the more recent rank‐metric minimal codes. We prove some bounds on their parameters, existence results, and, via a tool that we name geometric dual, we manage to construct minimal codes with few weights. A generalization of the celebrated Ashikhmin–Barg condition is proved and used to ensure the minimality of certain constructions.
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Dates and versions

hal-04746426 , version 1 (21-10-2024)

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Martino Borello, Ferdinando Zullo. Geometric dual and sum‐rank minimal codes. Journal of Combinatorial Designs, 2024, 32 (5), pp.238-273. ⟨10.1002/jcd.21934⟩. ⟨hal-04746426⟩
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