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Constacyclic codes of arbitrary lengths over ring \(Z_{p^m } + vZ_{p^m }\)

  • Published:
Journal of Electronics (China)

Abstract

By constructing a Gray map, constacyclic codes of arbitrary lengths over ring \(R = Z_{p^m } + vZ_{p^m }\) are studied, where v 2 = v The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular, (1+(v+1)αp)-constacyclic codes over R are classified in terms of generator polynomial, where α is a unit of \(Z_{p^m }\).

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References

  1. H. Q. Dinh and S. R. López-Permouth. Cyclic and negacyclic codes over finite chain rings. IEEE Transactions on Information Theory, 50(2004)8, 1728–1744.

    Article  MATH  Google Scholar 

  2. H. Q. Dinh. Constacyclic codes of length p s over \(F_{p^m } + uF_{p^m }\). Journal of Algebra, 324(2010)5, 940–950.

    Article  MATH  MathSciNet  Google Scholar 

  3. Liang Hua and Tang Yuansheng. Cyclic codes over ring \(F_{p^m } + uF_{p^m }\). Application Research of Computers, 27(2010)6, 2026–2027.

    Google Scholar 

  4. Li Ping and Zhu Shixin. Cyclic codes of arbitrary lengths over the ring F q + uF q . Journal of University of Science and Technology of China, 38(2008)12, 1392–1396.

    MATH  MathSciNet  Google Scholar 

  5. T. A. GulIiver and M. Harada. Codes over F 3 + uF 3 and improvements to the bounds on ternary linear codes. Designs Codes and Cryptography, 22 (2001)1, 89–96.

    Article  MathSciNet  Google Scholar 

  6. Zhu Shixin, Wang Yu and Shi Minjia. Some results on cyclic codes over F 2+vF 2. IEEE Transactions on Information Theory, 56(2010)4, 1680–1684.

    Article  MathSciNet  Google Scholar 

  7. Zhang Guanghui and Chen Bocong. Constacyclic Codes over F p+vF p arXiv preprint arXiv:1301.0669, 2013.

    Google Scholar 

  8. Zhu Shixin and Wang Liqi. A class of constacyclic codes over F p+vF p and its Gray image. Discrete Mathematics, 311(2011)23, 2677–2682.

    Article  MATH  MathSciNet  Google Scholar 

  9. Liao Dajian and Tang Yuansheng. A class of constacyclic codes over R+vR and its Gray image. International Journal of Communications, Network & System Sciences, 5(2012)4, 222–227.

    Article  Google Scholar 

  10. A. Sălăgean. Repeated-root cyclic and negacyclic codes over a finite chain ring. Discrete Applied Mathematics, 154(2006)2, 413–419.

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhu Shixin and Kai Xiaoshan. A class of constacyclic codes over \(Z_{p^m }\). Finite Fields and Their Applications, 16(2010)4, 243–254.

    Article  MATH  MathSciNet  Google Scholar 

  12. Zhu Shixin and Kai Xiaoshan. Dual and self-dual negacyclic codes of even length over \(Z_{2^a }\). Discrete Mathematics, 309(2009)8, 2382–2391.

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Correspondence to Lei Huang.

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Supported by the National Natural Science Foundation of China (No. 61370089).

Huang Lei, born in 1989, male, Master Degree.

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Huang, L., Zhu, S. Constacyclic codes of arbitrary lengths over ring \(Z_{p^m } + vZ_{p^m }\) . J. Electron.(China) 31, 222–226 (2014). https://doi.org/10.1007/s11767-014-3167-x

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  • DOI: https://doi.org/10.1007/s11767-014-3167-x

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