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Double bordered constructions of self-dual codes from group rings over Frobenius rings. (English) Zbl 1454.94126
A self-dual code $$C$$ satisfies $$C=C^\perp$$, where $$C^\perp$$ is the orthogonal under the Euclidian inner-product. The authors use a double bordered construction of self-dual codes using group rings and apply it when the groups are of order $$p$$ and $$2p$$, for prime $$p$$, over the rings $$F_2[u]/ \langle u^2 \rangle$$ and $$F_4[u]/ \langle u^2 \rangle$$. Using a Gray map they are able to construct new binary self-dual codes of lengths $$64$$, $$68$$ and $$80$$.
##### MSC:
 94B05 Linear codes (general theory) 94B15 Cyclic codes
Magma
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##### References:
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