On the smallest minimal blocking sets of image, for image an odd prime Original Research Article

We characterize the smallest minimal blocking sets of image, image an odd prime, in terms of ovoids of image and image. The proofs of these results are written for image since for these values it was known that every ovoid of image is an elliptic quadric. Recently, in Ball et al. (Des. Codes Cryptogr., to appear), it has been proven that for all image prime, every ovoid of image is an elliptic quadric. Since as many proofs as possible were written for general image, using the classification result of De Beule and Metsch (J. Combin. Theory Ser. A, 106 (2004) 327–333) on the smallest blocking sets of image, image prime, the results for image, image, image, are also valid for image prime, image. The case image is treated separately since this is the only value for image an odd prime for which image has an ovoid. We end the article by discussing the possibilities and remaining problems to obtain the characterization for general image odd.