On Kerdock codes

Claude Carlet

GREYC, Université de Caen
BP 105
78153 Le Chesnay Cedex, France

Finite Fields and their Applications~1997, Contemporary Mathematics 225, pages 155-163
American Mathematical Society, 1999


The Kerdock codes have been characterized as Z4-linear codes by A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé. We show how their weight distribution can be derived by connecting sums over the Teichmuller set to sums over the full Galois ring. We show also how the best known upper bound on their covering radius can be simply deduced from the computation of higher moments. We finally generalize a result from A.R. Calderbank and Gary McGuire concerning their projections on hyperplanes.