The paper's description is poor, but they seem to be describing an encoding where each of 20 possible amino acids are associated with a position within a string of 20 bits, e.g. alanine with offset 0, cysteine with offset 1, etc. With that representation, one amino acid residue within a window is encoded by a string of 20 bits, 19 of them being 0 and the other a 1; the single 1 bit occurring in the place corresponding to the residue.
This interpretation is supported by the paper's citation of Qian N, Sejnowski TJ (1998) "Predicting the secondary structure of globular
proteins using neural network models." J Mol Biol 202: 865–884. Qian's paper says:
Each group has 21 units, each unit representing 1 of the amino acids (or spacer). For a local encoding of the input sequence, 1 and only 1 input unit in each group, corresponding to the appropriate amino acid at each position, is given a value 1, and the rest are set to 0.