New extremal binary self-dual codes of length $68$ from $R_2$-lifts of binary self-dual codes

Suat Karadeniz; Bahattin Yildiz

doi:10.3934/amc.2013.7.219

Article Contents

2013, Volume 7, Issue 2: 219-229. Doi: 10.3934/amc.2013.7.219

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New extremal binary self-dual codes of length $68$ from $R_2$-lifts of binary self-dual codes

Suat Karadeniz^1, and
Bahattin Yildiz^1,

1.
Department of Mathematics, Fatih University, 34500, Istanbul

Received: December 31, 2012

Published: April 2013

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Abstract

A lift of binary self-dual codes to the ring $R_2$ is described. By using this lift, a family of self-dual codes over $R_2$ of length $17$ are constructed. Taking the binary images of these codes, extremal binary self-dual codes of length $68$ are obtained. For the first time in the literature, extremal binary codes of length $68$ with $\gamma=4$ and $\gamma = 6$ in $W_{68,2}$ have been obtained. In addition to these, six new codes with $\gamma = 0$ and fourteen new codes with $\gamma = 2$ in $W_{68,2}$ have also been found.

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Mathematics Subject Classification: Primary: 94B05; Secondary: 94B99.

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