Fixed-length encoding

Definition 8.48. A fixed-length encoding for a given family of groups (of prime order) has the following components ... 

Now a fixed-length encoding is given by the following components ... 

The outputs of a function Bf are elements of Dj, but the outputs of a hash function should be strings from a set 0, 1 "( ). Thus a fixed-length encoding for the elements of is needed, similar to Definition 8.48. However, the situation is much easier here, because it is not required that len(k) < k, and one can therefore take any natural encoding, without transformations between k and k. ... 

The length restriction (Definition 8.26b) implies that a fixed-length encoding exists for each claw-intractable family of permutation pairs. However, to base a construction on it, one must effectively know one. ... 

The function len is identical to length from the given fixed-length encoding, and so is the algorithm to compute it in unary. 

Before Construction 8.61 can be applied to the weak claw-intractable family of permutation pairs from Construction 8.64, a fixed-length encoding must be fixed. The sets to be encoded are RQR with I/1I2 2k. One can simply represent all their elements as binary numbers of length 2k with leading zeros. Furthermore, the standard prefix-free encoding, prefix Jree, is used for the messages. This yields the following construction. 

A way of encoding solutions to the problem—fixed length string of symbols... 

Autocorrelation is a technique that allows the compression of variable-length information into a fixed-length vector. The first application of this concept in the field of QSAR was presented by Moreau who proposed an autocorrelation function to encode the topology of a molecular graph ... 

A schematic representation of how the double-phase encoded DEPT pulse sequence achieves spatial and spectral resolution within the fixed bed of ion-exchange resin is shown in Fig. 45. Typical data acquired in this experiment are shown in Fig. 46. The data were recorded from a vertical section through the center of the bed. The direction of superficial flow was from the bottom to the top of the bed. The spectra shown were recorded at regular intervals along the length of the bed, with a spatial separation of approximately 2.5 mm. With reference to Fig. 46, the... 

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