Linear codes from ruled sets in finite projective spaces

Abstract

We construct linear codes from projective systems of a finite projective space, arising by considering the points of the lines connecting point-sets chosen and fixed in two complementary subspaces. This construction allows to look for linear codes by choosing appropriate sets to get immediately length and minimum distance.

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References

  1. 1.

    Huffman W.C.: Codes and groups. In: Pless V.S., Huffman W.C. (eds.) Handbook of Coding Theory, pp. 1345–1440. Elsevier, Amsterdam (1998).

    Google Scholar 

  2. 2.

    Kroll H.-J., Vincenti R.: PD-sets for the codes related to some classical varieties. Discret. Math. 301, 89–105 (2005).

    MathSciNet  Article  Google Scholar 

  3. 3.

    Kroll H.-J., Vincenti R.: PD-sets for binary RM-codes and the codes related to the Klein quadric and to the Schubert variety of PG(5, 2). Discret. Math. 308, 408–414 (2008).

    MathSciNet  Article  Google Scholar 

  4. 4.

    Napolitano V.: Note on a class of subsets of AG \((3, q)\) with intersection numbers \(1, q\) and \(n\) with respect to the planes. Geometry 2013(589362), 3 (2013).

    MATH  Google Scholar 

  5. 5.

    Tallini G.: Some new results on sets of type \((m, n)\) in projective planes. J. Geom. 29, 191–199 (1987).

    MathSciNet  Article  Google Scholar 

  6. 6.

    Tsfasman M.A., Vlâdut S.G.: Algebraic Geometric Codes. Kluwer, Amsterdam (1991).

    Book  Google Scholar 

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Correspondence to Rita Vincenti.

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Communicated by J. W. P. Hirschfeld.

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Kroll, HJ., Vincenti, R. Linear codes from ruled sets in finite projective spaces. Des. Codes Cryptogr. 88, 747–754 (2020). https://doi.org/10.1007/s10623-019-00707-9

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Keywords

  • Finite projective geometry
  • Projective systems
  • Linear codes

Mathematics Subject Classification

  • 51E22
  • 94B05