Decoding a Class of Alternant Codes for the Lee Metric

Following are the abstracts of contributions (i.e., talks and posters) to the 13th Annual Meeting of the IMS held at the National University of Ireland Maynooth, 6–8 September 2000. The abbreviations after the names designate: ‘M’ for main speaker, ‘S’ for speaker, ‘RS’ for research student, and ‘P’ for poster. The abstracts are included as provided by the contributors for this volume of the Bulletin, edited by the editor if deemed necessary. Harmonic Maps in Unfashionable Geometries F.E. Burstall, University of Bath (M) Many special surfaces in classical differential geometry are characterised by the property that an appropriate Gauss map is harmonic and then the integrable features of their geometry (spectral deformation, Bäcklund transformation, algebro-geometric solutions and so on) can be inferred from those of harmonic maps. Thus a special case of the Ruh–Vilms theorem asserts that a surface has constant mean curvature if and only if its Gauss map is a harmonic map into the 2-sphere and, similarly, a surface has constant negative Gauss curvature if and only if its Gauss map is Lorentz harmonic with respect to the metric induced on the surface by the second fundamental form. It is interesting that harmonic maps into pseudo-Riemannian symmetric spaces also arise in this context: a surface in S is Willmore if and only if its conformal Gauss map is harmonic. This is a map into the indefinite Grassmannian that parametrises 2-spheres in S and geometrically represents a congruence of 2-spheres having partial second order contact with the Willmore surface. In this talk I report on work in progress with Udo Hertrich-Jeromin and show that similar constructions are available in Lie sphere and projective differential geometry. Moreover, both geometries can be