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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
Software:
Magma
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References:
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