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New developments in q-polynomial codes

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Abstract

Cyclic codes are prominently used in electronics and communication engineering. A new view on cyclic codes based on q-polynomials has been introduced by Ding and Ling. This paper is concerned with new developments in cyclic codes from q-polynomials. The properties of the q-polynomial codes and the fundamental relations between q-polynomial codes and generator polynomials are proposed. Then a new design of t-error correcting codes is introduced. Several constructions of new q-polynomial codes from old ones are also presented.

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References

  1. Bose, R.C., Ray-Chaudhuri, D.K.: On a class of error correcting binary group codes. Inform. Control 3, 68–79 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chien, R.T.: Cyclic decoding procedure for the Bose-Chaudhuri-Hocquenghem codes. IEEE Trans. Inf. Theory 10(4), 357–363 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chien, R.T., Frazer, W.D.: An application of coding theory to document retrieval. IEEE Trans. Inf. Theory 12(2), 92–96 (1966)

    Article  Google Scholar 

  4. Ding, C., Ling, S.: A q-polynomial approach to cyclic codes. Finite Fields Appl. 20, 1–14 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Feng, G.L., Tzeng, K.K.: Decoding cyclic and BCH codes up to actual minimum distance using nonrecurrent syndrome dependence relations. IEEE Trans. Inf. Theory 37(6), 1716–1723 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gorenstein, D., Zierler, N.: A class of error-correcting codes in p m symbols. J. Soc. Ind. Applied Math 9(2), 207–214 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lemstra, H.W., Schoof, R.J.: Primitive normal bases for finite field. Math. Comput. 48(177), 217–231 (1987)

    Article  Google Scholar 

  8. Lidl, R., Niederreiter, H.: Finite Fields. Addison-Wesley Publishing Inc (1983)

  9. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North Holland Publishing Company, New York (1977)

    MATH  Google Scholar 

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Acknowledgments

The authors are very grateful to the editor and the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. State Key Laboratory of ISN, Xidian University, Xi’an, 710071, People’s Republic of China

    Chuan Lv & Guozhen Xiao

  2. School of Sciences, China University of Petroleum, Qingdao, 366580, People’s Republic of China

    Tongjiang Yan

Authors
  1. Chuan Lv
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  2. Tongjiang Yan
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  3. Guozhen Xiao
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Corresponding author

Correspondence to Chuan Lv.

Additional information

The work is supported by the National Natural Science Foundations of China (No.61170319), the Shandong Provincial Natural Science Foundation of China(No. ZR2014FQ005) and the Fundamental Research Funds for the Central Universities of China(No. 15CX02081A).

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Lv, C., Yan, T. & Xiao, G. New developments in q-polynomial codes. Cryptogr. Commun. 8, 103–112 (2016). https://doi.org/10.1007/s12095-015-0147-4

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  • DOI: https://doi.org/10.1007/s12095-015-0147-4

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