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The Horace Method for Error-Correcting Codes

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Abstract

Here we apply the so-called Horace method for zero-dimensional schemes to error-correcting codes on complete intersections. In particular, we obtain sharper estimates on the minimum distance.

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References

  1. Duursma I.M., Rentería C., Tapia-Recillas H. (2001). Reed-Muller codes on complete intersections. Appl Algebra Eng Comm Comput 11:455–462

    Article  MATH  Google Scholar 

  2. Eisenbud D., Green M., Harris J. (1996). Cayley–Bacharach theorems and conjectures. Bull Am Math Soc (N.S.) 33:295–324

    Article  MATH  MathSciNet  Google Scholar 

  3. Gold L., Little J., Schenck H. (2005). Cayley–Bacharach and evaluation codes on complete intersections. J Pure Appl Algebra 196:91–99

    Article  MATH  MathSciNet  Google Scholar 

  4. Hansen J.P. (1994). Points in uniform position and maximum distance separable codes Zero-dimensional schemes (Ravello, 1992). de Gruyter, Berlin pp 205–211

    Google Scholar 

  5. Hansen J.P. (2003). Linkage and codes on complete intersections. Appl Algebra Eng Comm Comput 14:175–185

    Article  MATH  Google Scholar 

  6. Hartshorne R. (1977). Algebraic geometry. Graduate texts in mathematics, vol. 52. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

  7. Hefez A. Kleiman S.L. (1985). Notes on the duality of projective varieties. Geometry today (Rome, 1984), Progress in Mathematics, vol 60. Birkhäuser, Boston, pp143–183

    Google Scholar 

  8. Hirschowitz A. (1985). La méthode d’Horace pour l’interpolation à plusieurs variables. Manuscripta Math 50:337–388

    Article  MATH  MathSciNet  Google Scholar 

  9. Migliore J.C. (1998). Introduction to liaison theory and deficiency modules. Progress in Mathematics, vol. 165, Birkhäuser, Boston

    MATH  Google Scholar 

  10. Rathmann J. (1987). The uniform position principle for curves in characteristic p. Math Ann 276:565–579

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38050, Povo (Trento), Italy

    Edoardo Ballico

  2. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Claudio Fontanari

Authors
  1. Edoardo Ballico
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  2. Claudio Fontanari
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Correspondence to Edoardo Ballico.

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Ballico, E., Fontanari, C. The Horace Method for Error-Correcting Codes. AAECC 17, 135–139 (2006). https://doi.org/10.1007/s00200-006-0012-y

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  • DOI: https://doi.org/10.1007/s00200-006-0012-y

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