A coding theoretic approach to extending designs (Q1896352)

One of the major links between coding theory and design theory is the study of designs held by the words of some fixed weight in a binary code. The authors consider the similar problem for a coset of a binary code. A second question that is studied is the extension of such designs. The results depend on theorems of \textit{W. O. Alltop} [Extending \(t\)-designs, J. Comb. Theory, Ser. A 18, 177--186 (1975; Zbl 0297.05028)] and on the Assmus-Mattson theorem. Several examples are given, notably for cosets of self-dual codes, e.g. 3-designs in the so-called baby Golay code. These can be extended to 5-designs related to the Golay code itself.