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Designs, Codes and Cryptography

Erschienen in:

31.03.2018

Linear codes over \(\mathbb {F}_{q}[x]/(x^2)\) and \(GR(p^2,m)\) reaching the Griesmer bound

verfasst von: Jin Li, Aixian Zhang, Keqin Feng

Erschienen in: Designs, Codes and Cryptography | Ausgabe 12/2018

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Abstract

We construct two series of linear codes C(G) over \(\mathbb {F}_{q}[x]/(x^2)\) and \(GR(p^2,m)\) reaching the Griesmer bound. Moreover, we consider the Gray images of C(G). The results show that the Gray images of C(G) over \(\mathbb {F}_{q}[x]/(x^2)\) are linear and also reach the Griesmer bound in some cases, and many of linear codes over \(\mathbb {F}_{q}\) we constructed have two Hamming (non-zero) weights.

Vorheriger Artikel A note on the weight spectrum of the Schubert code

Nächster Artikel Some results on generalized strong external difference families

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Titel: Linear codes over and reaching the Griesmer bound
verfasst von: Jin Li
Aixian Zhang
Keqin Feng
Publikationsdatum: 31.03.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 12/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0479-0

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