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Two New Infinite Families of 3-Designs from Kerdock Codes over Z4

Authors:	Kyeongcheol Yang Tor Helleseth

Institution:	(1) Department of Electronic Communication Engineering, Hanyang University, Seoul, 133-791, Korea;(2) Department of Informatics, University of Bergen, Hoyteknologisenteret, N-5020 Bergen, Norway

Abstract:	In this paper we show that the support of the codewords of each type in the Kerdock code of length 2^m over Z₄ form 3-designs for any odd integer $m \geqslant 3$ . In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer $m \geqslant 3$ . In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer $m \geqslant 3$ , whose parameters are $v = 2^m ,k = 2^{m - 1} + 2^{m - 2} \pm 2^{\frac{{m - 3}}{2}}$ ,and $\lambda = \frac{{k(k - 1)(k - 2)}}{{2^m - 2}}$ .

Keywords:	Linear codes over Z₄ Kerdock codes block designs
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