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The Dual Code of some Reed-Muller type Codes

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Abstract.

The dual code of some Reed-Muller type codes arising from the Veronese variety and Complete Intersections is determined. An example is given to illustrate the main result.

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References

  1. Delsarte, P., Goethals, J.M., MacWilliams, F.J.: On generalized Reed-Muller codes and their relatives. Inform. Control 16, 403–422 (1970)

    MATH  Google Scholar 

  2. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties and Algorithms. UTM, Springer, 1992

  3. Duursma, I., Rentería, C., Tapia-Recillas, H.: Reed Muller codes on Complete Intersections. AAECC 11, 455–462 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Geramita, A.V., Kreuzer, M., Robbiano, L.: Cayley Bacharach schemes and their canonical modules. Transactions of the AMS 339(1), 163–189 (1993)

    MATH  Google Scholar 

  5. Grayson, D.R., Stillman, M.: Macaulay2, 1998

  6. Hansen, J.P.: Zero-dimensional schemes. Proc. Int. Conf., Ravello, 1992. F. Orrechia and L. Chiantini (eds.), Walter de Gruyter, Berlin, 1994.

  7. Lachaud, G.: The parameters of the Projective Reed-Muller codes. Disc. Math. 81, 217–221 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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

  9. Rentería, C., Tapia-Recillas, H.: Linear codes associated to the ideal of points in P d and its canonical module. Commun. Algebra 24(3), 1083–1090 (1996)

    Google Scholar 

  10. Rentería, C., Tapia-Recillas, H.: Reed-Muller codes: An ideal Theory Approach. Commun. Algebra 25(2), 401–413 (1997)

    Google Scholar 

  11. Rentería, C., Tapia-Recillas, H.: The a- invariant of some Reed-Muller Codes. Appl. Algebra in Engng. Comm. Comput., AAECC 10(1), 33–40 (1999)

    Google Scholar 

  12. Sörensen, A.B.: Projective Reed-Muller Codes. IEEE Trans. on Inf. Theory 37(6), 1567–1576 (1991)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Escuela Superior de Fí sica y Matemáticas, Instituto Politécnico Nacional, 07300, México, D.F., Mexico

    M. González-Sarabia & C. Rentería

Authors
  1. M. González-Sarabia
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  2. C. Rentería
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Corresponding author

Correspondence to C. Rentería.

Additional information

Keywords: Reed-Muller type codes, Dual codes, Veronese variety, Complete intersection.

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González-Sarabia, M., Rentería, C. The Dual Code of some Reed-Muller type Codes. AAECC 14, 329–333 (2004). https://doi.org/10.1007/s00200-003-0136-2

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  • DOI: https://doi.org/10.1007/s00200-003-0136-2

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