Intersection sets, three-character multisets and associated codes

Abstract

In this article we construct new minimal intersection sets in \(\mathrm {AG}(r,q^2)\) sporting three intersection numbers with hyperplanes; we then use these sets to obtain linear error correcting codes with few weights, whose weight enumerator we also determine. Furthermore, we provide a new family of three-character multisets in \(\mathrm {PG}(r,q^2)\) with r even and we also compute their weight distribution.

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Correspondence to Luca Giuzzi.

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Communicated by V. A. Zinoviev.

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Aguglia, A., Giuzzi, L. Intersection sets, three-character multisets and associated codes. Des. Codes Cryptogr. 83, 269–282 (2017). https://doi.org/10.1007/s10623-016-0302-8

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Keywords

  • Quadric
  • Hermitian variety
  • Three-character set
  • Multiset
  • Error correcting code
  • Weight enumerator

Mathematics Subject Classification

  • 51E20
  • 94B05