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Designs, Codes and Cryptography
Erschienen in: Designs, Codes and Cryptography 12/2019

22.07.2019

Linear codes with small hulls in semi-primitive case

verfasst von: Claude Carlet, Chengju Li, Sihem Mesnager

Erschienen in: Designs, Codes and Cryptography | Ausgabe 12/2019

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Abstract

The hull of a linear code is defined to be the intersection of the code and its dual, and was originally introduced to classify finite projective planes. The hull plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism group of a linear code. It has been shown that these algorithms are very effective in general if the size of the hull is small. It is clear that the linear codes with the smallest hull are LCD codes and with the second smallest hull are those with one-dimensional hull. In this paper, we employ character sums in semi-primitive case to construct LCD codes and linear codes with one-dimensional hull from cyclotomic fields and multiplicative subgroups of finite fields. Some sufficient and necessary conditions for these codes are obtained, where prime ideal decompositions of prime p in cyclotomic fields play a key role. In addition, we show the non-existence of these codes in some cases.
Vorheriger Artikel Construction of resilient Boolean functions in odd variables with strictly almost optimal nonlinearity
Nächster Artikel Linear complementary dual codes over rings
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Metadaten
Titel
Linear codes with small hulls in semi-primitive case
verfasst von
Claude Carlet
Chengju Li
Sihem Mesnager
Publikationsdatum
22.07.2019
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 12/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-019-00663-4

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