Erratum to "Lattice constellation and codes from quadratic number fields" [IEEE Trans. Inform. Theory, vol. 47, No. 4, May. 2001]
Abstract
We correct a partial mistake for a metric presented in the article "Lattice constellation and codes from quadratic number fields" [IEEE Trans. Inform. Theory, vol. 47, No. 4, May. 2001]. We show that the metric defined in the article is not true, therefore, this brings about to destroy the encoding and decoding procedures. Also, we define a proper metric for some codes defined in the article and show that there exist some $1-$error correcting perfect codes with respect to this new metric.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2014
- DOI:
- 10.48550/arXiv.1411.7816
- arXiv:
- arXiv:1411.7816
- Bibcode:
- 2014arXiv1411.7816G
- Keywords:
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- Computer Science - Information Theory;
- 94B05;
- 94B60