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The number of self-dual codes over \({Z_{p^3}}\)

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Abstract

Let p be a prime number. In this paper, we consider codes over the ring \({Z_{p^3}}\) of integers modulo p 3 and give a characterization of self-duality. This leads to a construction of self-dual codes and a mass formula, which counts the number of such codes over \({Z_{p^3}}\) .

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References

  1. Balmaceda J.M., Betty R.A., Nemenzo F.: Mass formula for self-dual codes over \({Z_{p^2}}\) . Discrete Math. 308, 2984–3002 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Calderbank A.R., Sloane N.J.A.: Modular and p-adic cyclic codes. Des. Codes Cryptogr. 6, 21–35 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dougherty S.T., Harada M., Solé P.: Self-dual codes over rings and the Chinese remainder theorem. Hokkaido Math. J. 28, 253–283 (1999)

    MATH  MathSciNet  Google Scholar 

  4. Dougherty S.T., Gulliver T.A., Wong J.N.C.: Self-dual codes over Z 8 and Z 9. Des. Codes Cryptogr. 41, 235–249 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dougherty S.T., Gulliver T.A., Park Y.H., Wong J.N.C.: Optimal linear codes over Z m . J. Korean Math. Soc. 44, 1139–1162 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fields J., Gaborit P., Leon J., Pless V.: All self-dual Z 4 codes of length 15 or less are known. IEEE Trans. Inform. Theory 44, 311–322 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gaborit P.: Mass formulas for self-dual codes over Z 4 and F q  +  u F q rings. IEEE Trans. Inform. Theory 42, 1222–1228 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hammons A.R. Jr., Kumar P.V., Calderbank A.R., Sloane N.J.A., Solé P.: The Z 4 linearity of Kerdock, Preparata, Goethals and related codes. IEEE Trans. Inform. Theory 40, 301–319 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pless V.S.: The number of isotropic subspaces in a finite geometry. Atti. Accad. Naz. Lincei Rendic 39, 418–421 (1965)

    MATH  MathSciNet  Google Scholar 

  10. Pless V.S.: On the uniqueness of the Golay codes. J. Combin. Theory 5, 215–228 (1968)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Business Studies and Informatics, Daito Bunka University, Itabashi-ku, Tokyo, Japan

    Kiyoshi Nagata

  2. Institute of Mathematics, University of the Philippines, Diliman, Quezon City, Philippines

    Fidel Nemenzo

  3. Department of Mathematics, Sophia University, Chiyoda-ku, Tokyo, Japan

    Hideo Wada

Authors
  1. Kiyoshi Nagata
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  2. Fidel Nemenzo
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  3. Hideo Wada
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Corresponding author

Correspondence to Fidel Nemenzo.

Additional information

Communicated by V. A. Zinoviev.

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Nagata, K., Nemenzo, F. & Wada, H. The number of self-dual codes over \({Z_{p^3}}\) . Des. Codes Cryptogr. 50, 291–303 (2009). https://doi.org/10.1007/s10623-008-9232-4

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  • DOI: https://doi.org/10.1007/s10623-008-9232-4

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