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Infinite Families of 3-Designs from Z4-Goethals Codes with Block Size 8

Kalle Ranto, Infinite Families of 3-Designs from Z4-Goethals Codes with Block Size 8. SIAM Journal on Discrete Mathematics 15(3), 289–304, 2002.

Abstract:

We construct several new families of simple $3$-designs from
codewords of the Z_4-Goethals codes. These designs have parameters
3-(2^m,8,\lambda) with odd m >= 5. The smallest design has
\lambda=14(2^m-8)/3 and the others are corollaries of this and some
previously known designs. In the existence proofs we analyze the
low-weight codewords and count the number of solutions to certain
systems of equations over finite fields.

BibTeX entry:

@ARTICLE{jRanto02a,
  title = {Infinite Families of 3-Designs from Z4-Goethals Codes with Block Size 8},
  author = {Ranto, Kalle},
  journal = {SIAM Journal on Discrete Mathematics},
  volume = {15},
  number = {3},
  pages = {289–304},
  year = {2002},
  keywords = {t-esign, Goethals code, quaternary code, Kloosterman sum},
}

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

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