Classification of self-dual codes of length 20 over \(\mathbb{Z}_4\) and length at most 18 over \(\mathbb{F}_2+u\mathbb{F}_2\) (Q2177653)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of self-dual codes of length 20 over \(\mathbb{Z}_4\) and length at most 18 over \(\mathbb{F}_2+u\mathbb{F}_2\) |
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Classification of self-dual codes of length 20 over \(\mathbb{Z}_4\) and length at most 18 over \(\mathbb{F}_2+u\mathbb{F}_2\) (English)
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6 May 2020
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A self-dual code is a code that satisfies \(C=C^\perp.\) The residue code of a quaternary code \(C\) is \(\{ c \pmod{2} \ | \ c \in C \}\). Rains's algorithm classifies self-dual codes by studying their residue code. The authors use this algorithm to classify self-dual quaternary codes of length \(20\). The technique is extended to classify self-dual codes over \(F_2[u]/\langle u^2 \rangle\) of length \(n\) for \(8 \leq n \leq 18.\) For the entire collection see [Zbl 1428.94003].
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self-dual code
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self-orthogonal code
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automorphism group
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