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Cryptography and Communications

, Volume 9, Issue 2, pp 291–299 | Cite as

1-generator generalized quasi-cyclic codes over \(\mathbb {Z}_{4}\)

  • Tingting Wu
  • Jian GaoEmail author
  • Fang-Wei Fu
Article

Abstract

In this short paper, we determine the minimal generating set of 1-generator generalized quasi-cyclic codes over \(\mathbb {Z}_{4}\). We also determine their rank and introduce a lower bound for the minimum distance of free 1-generator generalized quasi-cyclic codes. Further, we construct some new \(\mathbb {Z}_{4}\)-linear codes and we obtain some good binary nonlinear codes using the usual Gray map.

Keywords

1-generator generalized quasi-cyclic codes New \(\mathbb {Z}_{4}\)-linear codes Gray map Good binary nonlinear codes 

Mathematics Subject Classification (2010)

94B05 94B15 

Notes

Acknowledgments

This research is supported by the National Key Basic Research Program of China (973 Program Grant No. 2013CB834204), the National Natural Science Foundation of China (Nos. 61571243, 61171082 and 61301137).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Chern Institute of Mathematics and LPMCNankai UniversityTianjinPeople’s Republic of China
  2. 2.School of ScienceShandong University of TechnologyZiboPeople’s Republic of China

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