In this article we present a class of codes with few weights arising from a special type of linear sets. We explicitly show the weights of such codes, their weight enumerators and possible choices for their generator matrices. In particular, our construction yields linear codes with three weights and, in some cases, almost MDS codes. The interest for these codes relies on their applications to authentication codes and secret schemes, and their connections with further objects such as association schemes and graphs.
CODES WITH FEW WEIGHTS ARISING FROM LINEAR SETS
Napolitano V.;Zullo F.
2020
Abstract
In this article we present a class of codes with few weights arising from a special type of linear sets. We explicitly show the weights of such codes, their weight enumerators and possible choices for their generator matrices. In particular, our construction yields linear codes with three weights and, in some cases, almost MDS codes. The interest for these codes relies on their applications to authentication codes and secret schemes, and their connections with further objects such as association schemes and graphs.File in questo prodotto:
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