According to Cayley's Theorem, the additive group [Z.sub.q] is isomorphic to a group of cyclic permutations
G, where x [member of] [Z.sub.q] corresponds to a cyclic permutation
that can be represented by an indicator vector with 1 in the (x + l)-th position.
Let Dom (p) denote the cyclic domain for a cyclic permutation
p [member of] Cyc ([sigma]).
[a.sub.n] [member of] L with [a.sub.i] [member of] T and we wish to generate the cyclic permutation
For the second code we used the hard decision Berlekamp-Massey decoder in the chasing technique and only the 63 cyclic permutation
in AutDAG with 100 generations (z=63, Ng=100).
If the assumption behind solving the problem stated that any cyclic permutation
of existing cycle combination considered as one cycle (for instance, cycle 1-2-3-4-1 is the same as 1-3-2-4-1) then applying the first phase of the thread-based cycle detection algorithm (parallel combination generator) will result a significant improvement over existing algorithms.
From the construction it follows that we are interested in properties that are invariant with respect to the cyclic permutation
(ABCD)(EFGH) of the labels.
One can easily verify from the above that other than [T.sub.d.sup.(4)][[T.sub.d.sup.(2)][x(n)]] and [T.sub.d.sup.(8)][x(n)], all other dyadically permuted sequences fall under the category of the cyclic permutation
class of x(n) and [x.sup.-1](n).
(Diangca) A labeled 3x3 Latin square is a group if the first row and first column entries are identical and the entries are precisely the cyclic permutation
of the standard sequence (ABC), namely (BCA) and (CAB).
Windless swindles make a neat cyclic permutation
Coy which one is cheated out of the freedom to raft?).
The invariance by the rotation factor can be obtained by a cyclic permutation
of the signature.
From these axioms, the basic "cyclic permutation
" rule follows immediately: [e.sub.1][e.sub.2] = i[e.sub.3]; [e.sub.2][e.sub.3] = i[e.sub.1]; [e.sub.3][e.sub.1] = i[e.sub.2]; where i = square root of -1
A cyclic permutation
is a permutation which is composed of a single n-cycle, when written in cycle notation.