S-structures on Lie algebras have been defined recently by Vinberg, as an extension of gradings by abelian groups. In this talk it will be shown how the exceptional simple Lie algebras of types E₇ and E₈are endowed with some SL₂ⁿ-structures, and are thus described very nicely in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so called code algebras. The involved codes are the simplex [7,3,4] and the extended Hamming [8,4,4] binary codes.

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