cosets - Produce cyclotomic cosets for Galois field
Syntax
cst = cosets(m)
Description
cst = cosets(m) produces
cyclotomic cosets mod 2^m-1. Each element of the
cell array cst is a Galois array that represents
one cyclotomic coset.
A cyclotomic coset is a set of elements that share the same
minimal polynomial. Together, the cyclotomic cosets mod 2^m-1 form
a partition of the group of nonzero elements of GF(2^m).
For more details on cyclotomic cosets, see the works listed in References.
Examples
The commands below find and display the cyclotomic cosets for
GF(8). As an example of interpreting the results, c{2} indicates
that A, A2, and A2 +
A share the same minimal polynomial, where A is a primitive element
for GF(8).
c = cosets(3);
c{1}'
c{2}'
c{3}'The output is below.
ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
Array elements =
1
ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
Array elements =
2 4 6
ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
Array elements =
3 5 7
See Also
minpol
References
[1] Blahut, Richard E., Theory
and Practice of Error Control Codes, Reading, MA, Addison-Wesley,
1983, p. 105.
[2] Lin, Shu, and Daniel J. Costello,
Jr., Error Control Coding: Fundamentals and Applications,
Englewood Cliffs, NJ, Prentice-Hall, 1983.
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