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Using the Lagrangian-Grassmannian, a smooth algebraic variety of dimension n(n + 1)/2 that parametrizes isotropic subspaces of dimension n in a symplectic vector space of dimension 2n, we construct a new class of linear codes generated by this variety, the Lagrangian-Grassmannian codes. We explicitly compute their word length, give a formula for their dimension and an upper bound for the minimum distance in terms of the dimension of the Lagrangian-Grassmannian variety.

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An alternate time-space framework is proposed by means of a hyperbolic scator algebraic formalism where the deformed Lorentz transformations are an immediate consequence of the formal properties of the algebra. We survey the group properties of the hyperbolic product in the restricted, super-restricted and zero magnitude subsets as well as in the complete scator set. Some properties of the magnitude are derived together with a decomposition of 1 + n dimensional scators in n products of scator elements with scalar component and only one non-vanishing director component. These results are used to describe the scator properties in 1 + n dimensions. The super-restricted subset is associated with superluminal frames or tachyons. The various compositions of subluminal and superluminal events in the same direction follow the canonical superluminal Lorentz transformations interpretation. Composition of orthogonal components produce novel results. Products of scators with components within and outside the light pyramid yield sub or super luminal scators as well as scators belonging to a mixed state.

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