[1]https://en.wikipedia.org/wiki/Linear-feedback_shift_register
   "In [2]computing, a linear-feedback shift register (LFSR) is a [3]shift
   register whose input bit is a [4]linear function of its previous state.
   The most commonly used linear function of single bits
   is [5]exclusive-or (XOR). Thus, an LFSR is most often a shift register
   whose input bit is driven by the XOR of some bits of the overall shift
   register value.
   The initial value of the LFSR is called the seed, and because the
   operation of the register is deterministic, the stream of values
   produced by the register is completely determined by its current (or
   previous) state. Likewise, because the register has a finite number of
   possible states, it must eventually enter a repeating cycle. However,
   an LFSR with a [6]well-chosen feedback function can produce a sequence
   of bits that appears random and has a [7]very long cycle.
   Applications of LFSRs include generating [8]pseudo-random
   numbers, [9]pseudo-noise sequences, fast digital counters,
   and [10]whitening sequences. Both hardware and software implementations
   of LFSRs are common.
   The mathematics of a [11]cyclic redundancy check, used to provide a
   quick check against transmission errors, are closely related to those
   of an LFSR."
   [end of quote]
              Jim Bell
   [12]× (BUTTON) (BUTTON)
     __________________________________________________________________

   From: James A. Donald <jamesd@echeque.com>
   To: cypherpunks@lists.cpunks.org
   Sent: Sunday, September 11, 2016 6:09 PM
   Subject: Permutations to scalars and back again.
   I need to be able to do two of the following three tasks.
   Generate a permutation of eighteen ones and eighteen zeros with equal
   probability for each permutation.  Or equivalently shuffle eighteen
   black cards and eighteen red cards.
   Sequentially generate all possible permutations with each permutation
   generated once and only once.
   Map between permutations and scalars, such that each permutation maps
   to
   unique number, and the set of numbers that represents valid
   permutations
   is dense.
   Could someone point me to the relevant literature, or literature for
   converting between different representations of a permutation?
   Since there are only two classes of items being shuffled, this class of
   permutations has a variety of special and convenient properties.

References

   1. https://en.wikipedia.org/wiki/Linear-feedback_shift_register
   2. https://en.wikipedia.org/wiki/Computing
   3. https://en.wikipedia.org/wiki/Shift_register
   4. https://en.wikipedia.org/wiki/Linear#Boolean_functions
   5. https://en.wikipedia.org/wiki/Exclusive-or
   6. https://en.wikipedia.org/wiki/Primitive_polynomial_(field_theory)
   7. https://en.wikipedia.org/wiki/Maximal_length_sequence
   8. https://en.wikipedia.org/wiki/Pseudorandomness
   9. https://en.wikipedia.org/wiki/Pseudorandom_noise
  10. https://en.wikipedia.org/wiki/Whitening_sequences
  11. https://en.wikipedia.org/wiki/Cyclic_redundancy_check
  12. file:///var/lib/mailman/archives/private/cypherpunks/attachments/20160912/c2d32e4f/attachment-tmp.html