Abstract
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 \(\mathbb F _2+u\mathbb F _2\). 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.
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The authors would like to thank the reviewers for their useful comments which improved the paper considerably. In addition, we would like to thank the Editor for their careful handling of our paper.
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Communicated by J.-L. Kim.
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Guenda, K., Gulliver, T.A. & Sheikholeslam, S.A. Lexicodes over rings. Des. Codes Cryptogr. 72, 749–763 (2014). https://doi.org/10.1007/s10623-012-9791-2
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DOI: https://doi.org/10.1007/s10623-012-9791-2