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Designs, Codes and Cryptography

Erschienen in:

10.02.2017

\({{\mathbb {Z}}}_2\)-double cyclic codes

verfasst von: Joaquim Borges, Cristina Fernández-Córdoba, Roger Ten-Valls

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2018

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A binary linear code C is a \({\mathbb {Z}}_2\)-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the \({\mathbb {Z}}_2[x]\)-module \({\mathbb {Z}}_2[x]/(x^r-1)\times {\mathbb {Z}}_2[x]/(x^s-1).\) We determine the structure of \({\mathbb {Z}}_2\)-double cyclic codes giving the generator polynomials of these codes. We give the polynomial representation of \({\mathbb {Z}}_2\)-double cyclic codes and its duals, and the relations between the generator polynomials of these codes. Finally, we study the relations between \({{\mathbb {Z}}}_2\)-double cyclic and other families of cyclic codes, and show some examples of distance optimal \({\mathbb {Z}}_2\)-double cyclic codes.

Vorheriger Artikel On Bonisoli’s theorem and the block codes of Steiner triple systems

Nächster Artikel Strengthening the security of authenticated key exchange against bad randomness

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Titel: -double cyclic codes
verfasst von: Joaquim Borges
Cristina Fernández-Córdoba
Roger Ten-Valls
Publikationsdatum: 10.02.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0334-8

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