Publications [#235790] of Robert Calderbank

Journal articles or Book chapters PUBLISHED
  1. Calderbank, AR; Goethals, J-M, THREE-WEIGHT CODES AND ASSOCIATION SCHEMES., Philips Journal of Research, vol. 39 no. 4-5 (1984), pp. 143-152 .

    Three-weight projective codes C are considered for which the restriction to C of the Hamming association scheme H//n(q) is an association scheme with three classes. Sufficient conditions are established and restrictions on the three weights of C are obtained. It is shown in the binary case that the three-weight subcodes of the shortened second-order Reed-Muller codes provide a large class of examples, Previously known examples were the duals of perfect 3-error-correcting or uniformly packed 2-error-correcting codes.