Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ONE GENERATOR QUASI-CYCLIC CODES OVER 𝔽2 + v𝔽2

  • OZEN, MEHMET (Department of Mathematics, Faculty of Science and Arts, Sakarya University) ;
  • OZZAIM, N. TUGBA (Department of Mathematics, Faculty of Science and Arts, Sakarya University) ;
  • AYDIN, NUH (Department of Mathematics and Statistics, Kenyon College)
  • Received : 2017.06.20
  • Accepted : 2018.04.27
  • Published : 2018.09.30
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Abstract

In this paper, we investigate quasi-cyclic codes over the ring $R={\mathbb{F}}_2+v{\mathbb{F}}_2$, where $v^2=v$. We investigate the structure of generators for one-generator quasi-cyclic codes over R and their minimal spanning sets. Moreover, we find the rank and a lower bound on minimum distances of free quasi-cyclic codes over R. Further, we find a relationship between cyclic codes over a different ring and quasi-cyclic codes of index 2 over R.

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References

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