Lexicodes over rings. (English) Zbl 1321.94143
Summary: In this paper, we consider the construction of linear lexicodes over finite chain rings by using a \(B\)-ordering over these rings and a selection criterion. As examples we give lexicodes over \(\mathbb Z_4\) and \(\mathbb F_2+u\mathbb F F_2\). It is shown that this construction produces many optimal codes over rings and also good binary codes. Some of these codes meet the Gilbert bound. We also obtain optimal self-dual codes, in particular the octacode.
MSC:
| 94B65 | Bounds on codes |
| 94B05 | Linear codes (general theory) |
| 16T99 | Hopf algebras, quantum groups and related topics |
References:
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