Abstract
In this paper we study \({{\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}}\)-additive codes, which are extensions of recently introduced \(\mathbb {Z}_{2}\mathbb {Z}_{4}\)-additive codes. We determine the standard forms of the generator and parity-check matrices of \({{\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}}\)-additive codes. Moreover, we investigate \({{\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}}\)-cyclic codes and give their generator polynomials and spanning sets. We also give some illustrative examples of both \({{\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}}\)-additive codes and \({{\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}}\)-cyclic codes.
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The authors would like to thank the anonymous reviewers for their valuable remarks that led to an improved version of the paper.
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Aydogdu, I., Gursoy, F. \({\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}\)-Cyclic codes. J. Appl. Math. Comput. 60, 327–341 (2019). https://doi.org/10.1007/s12190-018-01216-z
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DOI: https://doi.org/10.1007/s12190-018-01216-z
Keywords
- Generator matrix
- Parity-check matrix
- Cyclic codes
- \({{\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}}\)-additive codes