Kyeongcheol Yang

On the weight hierarchy of Kerdock codes over Z/sub 4/

The rth generalized Hamming weight d/sub r/ of the Kerdock code of length 2/sup m/ over Z/sub 4/ is considered. A lower bound on d/sub r/ is derived for any r, and d/sub r/ is exactly determined for r=0.5, 1, 1.5, 2, 2.5. In the case of length 2/sup 2m/, d/sub r/ is determined for any r, where 0/spl les/r/spl les/m and 2r is an integer. In addition, it is shown that it is sometimes possible to determine the generalized Hamming weights of the Kerdock codes of larger length using the results of d/sub r/ for a given length. The authors also provide a closed-form expression for the Lee weight of a Kerdock codeword in terms of the coefficients in its trace expansion.

An Infinite Family of 3-Designs from Preparata Codes over Z_4

We show that the support of minimum Lee weight codewords having Hamming weight 5 in the Preparata code over Z4 form a 3-(2m,5,10) design for any odd integer m ≥ 3.

On the weight hierarchy of Goethals codes over Z/sub 4/

The rth generalized Hamming weight d/sub r/(m,j) of the Goethals code /spl Gscr//sub m/(j) of length 2/sup m/ over Z/sub 4/ is considered in this correspondence. In the case that m/spl ges/3 is an odd integer, d/sub r/(m,j) is exactly determined for r=0.5, 1, 1.5, 2, 2.5, and 3.0. For a composite m, we give an upper bound d/sub r/(m,j) using the lifting technique.

Two New Infinite Families of 3-Designs from Kerdock Codesover \mbox{ Z } _4

AbstractIn this paper we show that the support of the codewords of each type in the Kerdock code of length 2m over Z4 form 3-designs for any odd integer

Kerdock codes over Z/sub 4/ and their application to designs

m \geqslant 3

On the minimum support weights of Goethals codes over Z/sub 4/

. In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer

Sequences and Their Applications SETA 2006: 4th International Conference, Beijing, China, September 24-28, 2006,Proceedings (Lecture Notes in Computer Science)

m \geqslant 3