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arXiv · 1406.1281

On codes over R_{k,m} and constructions for new binary self-dual codes

Nesibe Tufekci·Bahattin Yildiz
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Abstract

In this work, we study codes over the ring R_{k,m}=F_2[u,v]/ , which is a family of Frobenius, characteristic 2 extensions of the binary field. We introduce a distance and duality preserving Gray map from R_{k,m} to F_2^{km} together with a Lee weight. After proving the MacWilliams identities for codes over R_{k,m} for all the relevant weight enumerators, we construct many binary self-dual codes as the Gray images of self-dual codes over R_{k,m}. In addition to many extremal binary self-dual codes obtained in this way, including a new construction for the extended binary Golay code, we find 175 new Type I binary self-dual codes of parameters [72,36,12] and 105 new Type II binary self-dual codes of parameter [72,36,12].

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Nesibe Tufekci, Bahattin Yildiz. 2014-06-05. On codes over R_{k,m} and constructions for new binary self-dual codes. https://arxiv.org/abs/1406.1281

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