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3-Designs from Z4-Goethals-Like Codes and Variants of Cyclotomic Polynomials

Jyrki Lahtonen, Kalle Ranto, Roope Vehkalahti, 3-Designs from Z4-Goethals-Like Codes and Variants of Cyclotomic Polynomials. In: Proceedings of the International Workshop on Coding and Cryptography WCC'2005 , 425-434, 2005.

Abstract:

We construct families of simple 3-(2^m,8,14(2^m-8)/3) designs
with odd m>=5 from codewords of Z4-Goethals-like
codes G(k) where k=2^l and l>=1. In addition, these designs
imply also the existence of the other design families constructed from
the Z4-Goethals codes G(1) by Ranto. In the existence proofs we
count the number of solutions to certain systems of equations over
finite fields and use Dickson polynomials and variants of cyclotomic
polynomials and identities connecting them.

BibTeX entry:

@INPROCEEDINGS{inpLaRaVe05a,
  title = {3-Designs from Z4-Goethals-Like Codes and Variants of Cyclotomic Polynomials},
  booktitle = {Proceedings of the International Workshop on Coding and Cryptography WCC'2005 },
  author = {Lahtonen, Jyrki and Ranto, Kalle and Vehkalahti, Roope},
  pages = {425-434},
  year = {2005},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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