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Reed-Muller Codes on Complete Intersections

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

By using results and techniques from commutative algebra such as the vanishing ideal of a set of points, its a-invariant, the Hilbert polynomial and series, as well as finite free resolutions and the canonical module, some results about Reed-Muller codes defined on a zero-dimensional complete intersection in the n-projective dimensional space are given. Several examples of this class of codes are presented in order to illustrate the ideas.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801, USA (e–mail: duursma@math.uiuc.edu), , , , , , US

    I. M. Duursma

  2. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, 07300 México, D.F., México (e–mail: renteri@esfm.ipn.mx), , , , , , MX

    C. Rentería

  3. Departamento de Matemáticas, Universidad Autónoma Metropolitana–I, 09340 México, D.F., México, (e–mail: htr@xanum.uam.mx), , , , , , MX

    H. Tapia-Recillas

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  1. I. M. Duursma
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  2. C. Rentería
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  3. H. Tapia-Recillas
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Received: March 11, 1999; revised version: November 6, 2000

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Duursma, I., Rentería, C. & Tapia-Recillas, H. Reed-Muller Codes on Complete Intersections. AAECC 11, 455–462 (2001). https://doi.org/10.1007/s002000000047

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  • DOI: https://doi.org/10.1007/s002000000047