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 <jam...@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.
