Kerdock codes over Z/sub 4/ and their application to designs
Kyeongcheol Yang, Tor Helleseth · 2002
We show that the support of the codewords of each type in the Kerdock code of length 2/sup m/ over Z/sub 4/ form 3-designs for any add integer m/spl ges/3. In particular, two new infinite families of 3-designs are obtained in this construction for any odd integer m/spl ges/3, whose parameters are v=2/sup m/, k=2/sup m-1/+2/sup m-2//spl plusmn/2/sup (m-3)/2/, and /spl lambda/=k(k-1)(k-2)/2/sup m/-2.