Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

Synthesis of Iron Oxide Nanoparticles Used as MRI Contrast Agents: A Parametric Study

Colloidal iron oxides play an important role as magnetic resonance imaging (MRI) contrast agents. The superparamagnetic particles actually used are constituted by solid cores (diameter of 5-15 nm), generally coated by a thick polysaccharidic layer (hydrodynamic radii of 30-100 nm), and formulated by direct coprecipitation of iron salts in the presence of polymeric material. To better control the synthesis, we attempted to formulate new stable uncoated superparamagnetic nanoparticles. Colloids were generated by coprecipitation of an aqueous solution of iron salts and tetramethylammonium hydroxide (TMAOH) solution. The influence of parameters such as media composition, iron media, injection fluxes, Fe and TMAOH concentrations, temperature, and oxygen on size, magnetic and magnetic resonance relaxometric properties, and colloidal stability of particles were evaluated. We have determined the relative importance of these parameters as well as the optimal conditions for obtaining uncoated stable particles with an average size of 5 nm and interesting relaxivities. The interpretation of the observed limits takes into account diffusibilities of reactants and product, feeding rates of reactants, and surface properties of nanoparticles. A model of synthesis, related to spontaneous emulsification of suspensions, is proposed. Copyright 1999 Academic Press.