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Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes

Daniele Bartoli (UGent) , Adnen Sboui and Leo Storme (UGent)
(2016) ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 10(2). p.355-365
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Abstract
We present bounds on the number of points in algebraic curves and algebraic hypersurfaces in P-n(F-q) of small degree d, depending on the number of linear components contained in such curves and hypersurfaces. The obtained results have applications to the weight distribution of the projective Reed-Muller codes PRM(q, d, n) over the finite field IFq.
Keywords
quadrics, Algebraic varieties, small weight codewords, intersections, projective Reed-Muller codes, P-N(F-Q), ARCS

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MLA
Bartoli, Daniele, et al. “Bounds on the Number of Rational Points of Algebraic Hypersurfaces over Finite Fields, with Applications to Projective Reed-Muller Codes.” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 10, no. 2, 2016, pp. 355–65, doi:10.3934/amc.2016010.
APA
Bartoli, D., Sboui, A., & Storme, L. (2016). Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 10(2), 355–365. https://doi.org/10.3934/amc.2016010
Chicago author-date
Bartoli, Daniele, Adnen Sboui, and Leo Storme. 2016. “Bounds on the Number of Rational Points of Algebraic Hypersurfaces over Finite Fields, with Applications to Projective Reed-Muller Codes.” ADVANCES IN MATHEMATICS OF COMMUNICATIONS 10 (2): 355–65. https://doi.org/10.3934/amc.2016010.
Chicago author-date (all authors)
Bartoli, Daniele, Adnen Sboui, and Leo Storme. 2016. “Bounds on the Number of Rational Points of Algebraic Hypersurfaces over Finite Fields, with Applications to Projective Reed-Muller Codes.” ADVANCES IN MATHEMATICS OF COMMUNICATIONS 10 (2): 355–365. doi:10.3934/amc.2016010.
Vancouver
1.
Bartoli D, Sboui A, Storme L. Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes. ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 2016;10(2):355–65.
IEEE
[1]
D. Bartoli, A. Sboui, and L. Storme, “Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes,” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 10, no. 2, pp. 355–365, 2016.
@article{8028382,
  abstract     = {{We present bounds on the number of points in algebraic curves and algebraic hypersurfaces in P-n(F-q) of small degree d, depending on the number of linear components contained in such curves and hypersurfaces. The obtained results have applications to the weight distribution of the projective Reed-Muller codes PRM(q, d, n) over the finite field IFq.}},
  author       = {{Bartoli, Daniele and Sboui, Adnen and Storme, Leo}},
  issn         = {{1930-5346}},
  journal      = {{ADVANCES IN MATHEMATICS OF COMMUNICATIONS}},
  keywords     = {{quadrics,Algebraic varieties,small weight codewords,intersections,projective Reed-Muller codes,P-N(F-Q),ARCS}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{355--365}},
  title        = {{Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes}},
  url          = {{http://doi.org/10.3934/amc.2016010}},
  volume       = {{10}},
  year         = {{2016}},
}
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