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arXiv · 1405.7147

New extremal binary self-dual codes from F_4 + uF_4-lifts of quadratic double circulant codes over F_4

Abidin Kaya·Bahattin Yildiz·Irfan Siap
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Abstract

In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension theorems as well as the ring extension version are used to obtain 7 extremal self-dual binary codes of length 58, 24 extremal self-dual binary codes of length 66 and 29 extremal self-dual binary codes of length 68, all with new weight enumerators, updating the list of all the known extremal self-dual codes in the literature.

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Abidin Kaya, Bahattin Yildiz, Irfan Siap. 2014-05-28. New extremal binary self-dual codes from F_4 + uF_4-lifts of quadratic double circulant codes over F_4. https://doi.org/10.1016/j.ffa.2015.05.004

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