Rank-metric codes, linear sets, and their duality
J Sheekey, G Van de Voorde - Designs, Codes and Cryptography, 2020 - Springer
Designs, Codes and Cryptography, 2020•Springer
In this paper we investigate connections between linear sets and subspaces of linear maps.
We give a geometric interpretation of the results of Sheekey (Adv Math Commun 10: 475–
488, 2016, Sect. 5) on linear sets on a projective line. We extend this to linear sets in
arbitrary dimension, giving the connection between two constructions for linear sets defined
in Lunardon (J Comb Theory Ser A 149: 1–20, 2017). Finally, we then exploit this connection
by using the MacWilliams identities to obtain information about the possible weight …
We give a geometric interpretation of the results of Sheekey (Adv Math Commun 10: 475–
488, 2016, Sect. 5) on linear sets on a projective line. We extend this to linear sets in
arbitrary dimension, giving the connection between two constructions for linear sets defined
in Lunardon (J Comb Theory Ser A 149: 1–20, 2017). Finally, we then exploit this connection
by using the MacWilliams identities to obtain information about the possible weight …
Abstract
In this paper we investigate connections between linear sets and subspaces of linear maps. We give a geometric interpretation of the results of Sheekey (Adv Math Commun 10:475–488, 2016, Sect. 5) on linear sets on a projective line. We extend this to linear sets in arbitrary dimension, giving the connection between two constructions for linear sets defined in Lunardon (J Comb Theory Ser A 149:1–20, 2017). Finally, we then exploit this connection by using the MacWilliams identities to obtain information about the possible weight distribution of a linear set of rank n on a projective line .
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