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

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 $\lambda = \frac{{k(k - 1)(k - 2)}}{{2^m - 2}}$.