1. A digital decoder for a transmitting-and-receiving-multi-antenna digital wireless transmission chain, for determining symbols transmitted in linear space-time coded transmission signals based on a convolutional binary coding, this digital decoder being fed by: a received symbols signal vector Z, and a matrix C resulting from the product of a transmission channel matrix H and a space-time coding matrix M for the transmission comprising: a comprehensive space-time decoder for calculating the metric between each possible codeword and the received symbols signal vector Z, and for generating as output all the metrics thus calculated; and a binary decoder for determining, by using all the metrics generated as probabilities of transitions between states of the binary decoder, the most probable path taken during the convolutional coding, and for deducing from these the symbols transmitted.