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Cyclic Generalized Separable (L, G) Codes

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Coding Theory and Applications

Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 3))

Abstract

A new class of cyclic generalized separable (L, G) codes is constructed.

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References

  1. Goppa,V.D.: A new class of linear error-correcting codes. Probl. Inf. Trans. 6(3), 24–30 (1970)

    Google Scholar 

  2. Berlecamp, E.R., Moreno, O.: Extended double-error-gorrecting binary Goppa codes are cyclic. IEEE Trans. Inf. Theory 19(6), 817–818 (1973)

    Article  Google Scholar 

  3. Tzeng, K.K., Zimmermann, K.: On extending Goppa codes to cyclic codes. IEEE Trans. Inf. Theory 21(6), 712–716 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  4. Tzeng, K.K., Yu, C.Y.: Characterization theorems for extending Goppa codes to cyclic codes. IEEE Trans. Inf. Theory 25(2), 246–250 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  5. Moreno, O.: Symmetries of binary Goppa codes. IEEE Trans. Inf. Theory 25(5), 609–612 (1979)

    Article  MATH  Google Scholar 

  6. Vishnevetskii, A.L.: Cyclicity of extended Goppa codes. Probl. Pered. Inf. 18(3), 14–18 (1982)

    MathSciNet  Google Scholar 

  7. Stichenoth, H.: Wich extended Goppa codes are cyclic? J. Comb. Theory A 51, 205–220 (1989)

    Google Scholar 

  8. B erger, T.P.: Goppa and related codes invariant under a prescribed permutation. IEEE Trans. Inf. Theory 46(7), 2628–2633 (2000)

    Google Scholar 

  9. Berger, T.P.: On the cyclicity of Goppa codes, parity-check subcodes of Goppa codes, and extended Goppa codes. Finite Fields Appl. 6, 255–281 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Berger, T.P.: Quasi-cyclic Goppa codes. In: Proceedings of ISIT2000, Sorrente, p. 195 (2000)

    Google Scholar 

  11. Berger, T.P.: New classes of cyclic extended Goppa codes. IEEE Trans. Inf. Theory 45(4), 1264–1266 (1999)

    Article  MATH  Google Scholar 

  12. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  13. Bezzateev, S., Shekhunova, N.: Subclass of cyclic Goppa codes. IEEE Trans. Inf. Theory 59(11), 7379–7385 (2013)

    Article  MathSciNet  Google Scholar 

  14. Shekhunova, N.A., Mironchikov, E.T.: Cyclic (L, g)-codes. Probl. Pered. Inf. 17(2), 3–9 (1981)

    Google Scholar 

  15. Bezzateev, S.V., Shekhunova, N.A.: One generalization of Goppa codes. In: Proceedings of ISIT-97, Ulm, p. 299 (1997)

    Google Scholar 

  16. Zeh, A., Wachter-Zeh, A., Bezzateev, S.: Decoding cyclic codes up to a new bound on the minimum distance. IEEE Trans. Inf. Theory 58(6), 3951–3960 (2012)

    Article  MathSciNet  Google Scholar 

  17. Zeh, A., Bezzateev, S.: A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes. Designs Codes Cryptogr. 71, 229–246 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Sergey Bezzateev .

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Bezzateev, S. (2015). Cyclic Generalized Separable (L, G) Codes. In: Pinto, R., Rocha Malonek, P., Vettori, P. (eds) Coding Theory and Applications. CIM Series in Mathematical Sciences, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-17296-5_5

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