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Some new binary quasi-cyclic codes from codes over the ring \(\mathbb F _2+u\mathbb F _2+v\mathbb F _2+uv\mathbb F _2\)

  • Nuh Aydin
  • Suat Karadeniz
  • Bahattin YildizEmail author
Original Paper

Abstract

We consider quasi-cyclic codes over the ring \(\mathbb{F }_2+u\mathbb{F }_2+v\mathbb{F }_2+uv\mathbb{F }_2\), a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.

Keywords

Lee weight Gray maps Cyclic codes Quasi-cyclic codes 

Mathematics Subject Classification (2000)

94B15 94B05 13P05 

Notes

Acknowledgments

The authors would like to thank the anonymous referees for their valuable remarks and suggestions that improved the presentation of this paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsKenyon CollegeGambierUSA
  2. 2.Department of MathematicsFatih UniversityIstanbulTurkey

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