On the Optimality of the Regular Simplex Code
Henry J. Landau, David Slepian · Bell System Technical Journal · 1966
We prove here the long conjectured fact that the regular simplex is the code of minimal error probability for transmission over the infinite-band Gaussian channel. The code is actually optimal for a rather wide class of assumed channel noises. We also establish the optimality of several other codes for the band-limited Gaussian channel.