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\({\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}\)-Cyclic codes

  • Ismail AydogduEmail author
  • Fatmanur Gursoy
Original Research
  • 110 Downloads

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.

Keywords

Generator matrix Parity-check matrix Cyclic codes \({{\mathbb {Z}}_{2}{\mathbb {Z}}_{4}{\mathbb {Z}}_{8}}\)-additive codes 

Mathematics Subject Classification

94B05 94B60 

Notes

Acknowledgements

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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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of MathematicsYildiz Technical UniversityIstanbulTurkey

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