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Enumeration of Kerdock codes of length 64

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Abstract

An algorithm for enumerating Kerdock codes is discussed and used to show that the Kerdock code of length 64 is unique up to equivalence.

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References

  1. Borges J., Fernandez C., Phelps K.T.: QRM codes. IEEE Trans. Inf. Theory 54(1), 380–386 (2008).

  2. Borges J., Phelps K.T., Rifa J., Zinoviev V.: On \({\mathbb{Z}}_4\)-linear Preparata-like and Kerdock-like codes. IEEE Trans. Inf. Theory 49(11), 2834–2843 (2003).

  3. Calderbank A.R., Cameron P.J., Kantor W.M., Seidel J.J.: \({\mathbb{Z}}_4\)-Kerdock codes, orthogonal spreads, and extremal Euclidean line-sets. Proc. Lond. Math. Soc. (3) 75(2), 436–480 (1997).

  4. Carlet C., Yucas J.: Piecewise constructions of bent and almost optimal Boolean functions. Des. Codes Cryptogr. 37, 449–464 (2005).

  5. Hammons A.R., Kumar P.V., Calderbank A.R., Sloane N.J.A., Sole P.: The \({\mathbb{Z}}_{4}\)-linearity of Kerdock, Preparata, Goethals and related codes. IEEE Trans. Inf. Theory 40, 301–319 (1994).

  6. Kantor W.M.: An exponential number of generalized Kerdock codes. Inf. Control 53, 74–80 (1982).

  7. Kantor W. M.: Codes, quadratic forms and finite geometries. Different Aspects of Coding Theory (San Francisco, CA, 1995). In: Proceedings of the Symposia in Applied Mathematics, vol. 50, pp. 153–177. American Mathematical Society, Providence (1995).

  8. Kantor W.M., Williams M.E.: Symplectic semi-field planes and \({\mathbb{Z}}_4\)-linear codes. Trans. Am. Math. Soc. 356(3), 895–938 (2003).

  9. Kerdock A.M.: A class of low rate nonlinear binary codes. Inf. Control 20, 182–187 (1972).

  10. MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1997).

  11. Preparata F.P.: A class of optimum nonlinear double-error correcting codes. Inf. Control 13, 378–400 (1968).

  12. Rothaus O.S.: On bent functions. J. Comb. Theory Ser. A 20(3), 300–305 (1976).

  13. Semakov N.V., Zinoviev V.A., Zaitsev G.V.: On duality of Preparata and Kerdock codes. In: Proceedings of the Fifth All-Union Conference on Coding Theory, Part 2, Moscow-Gorkyi, Moscow, pp. 55–58 (1972).

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  1. Mathematics and Statistics Department, Auburn University, Auburn, AL, 36849, USA

    Kevin Phelps

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  1. Kevin Phelps
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Correspondence to Kevin Phelps.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Cryptography, Codes, Designs and Finite Fields: In Memory of Scott A. Vanstone”.

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Phelps, K. Enumeration of Kerdock codes of length 64. Des. Codes Cryptogr. 77, 357–363 (2015). https://doi.org/10.1007/s10623-015-0053-y

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  • DOI: https://doi.org/10.1007/s10623-015-0053-y

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