Permutations to scalars and back again.

[jim bell]

https://en.wikipedia.org/wiki/Linear-feedback_shift_register
"In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state.The most commonly used linear function of single bits is 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 well-chosen feedback function can produce a sequence of bits that appears random and has a very long cycle.Applications of LFSRs include generating pseudo-random numbers, pseudo-noise sequences, fast digital counters, and whitening sequences. Both hardware and software implementations of LFSRs are common.The mathematics of a 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
×   


      From: James A. Donald <jamesd at echeque.com>
 To: cypherpunks at 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.





   
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