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Designs, Codes and Cryptography

, Volume 83, Issue 2, pp 269–282 | Cite as

Intersection sets, three-character multisets and associated codes

  • Angela Aguglia
  • Luca Giuzzi
Article
  • 128 Downloads

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.

Keywords

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

Mathematics Subject Classification

51E20 94B05 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mechanics, Mathematics and ManagementPolitecnico di BariBariItaly
  2. 2.Section of Mathematics, D.I.C.A.T.A.M.Università di BresciaBresciaItaly

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