Quasi-symmetric designs and codes meeting the Grey-Rankin bound (Q1356042)

A characterization of the parameters of binary codes meeting the Grey-Rankin bound is proved. As pointed out earlier by \textit{D. Jungnickel} and the reviewer [Des. Codes Cryptography 1, No. 3, 247-253 (1991; Zbl 0766.05009)], quasi-symmetric designs with the property that the symmetric difference of any two blocks is either a block or a complement of a block give rise to linear codes meeting the Grey-Rankin bound. The present characterization implies that all linear binary codes meeting the Grey-Rankin bound are of this type.