The public-key is G' = SGP, where G is a k x n generator matrix for the Goppa code, S is a k x k non-singular matrix, and P is an n x n
permutation matrix. In addition, the private keys are S, G, and P.
, [j.sub.#J]} yields a
permutation matrix [P.sub.J] with entries [p.sub.ij] = 0 for i,j = 1, ..., n, except [mathematical expression not reproducible] for i = 1, ...
It can be shown that the optimal linear processing matrix of the special "relay" is a promotion of the
permutation matrix. To maximize the system throughput under fixed power allocation, the optimal linear processing matrix should be found out.
[PI] is a
permutation matrix. [[DELTA].sub.i], i =1, ..., 3, are diagonal scaling matrices satisfying [[DELTA].sub.1] [[DELTA].sub.2] [[DELTA].sub.3] = [I.sub.K]
A matrix A is called reducible if there exists an n order
permutation matrix P such that
Two pivot orderings O, O' [member of] O([P.sub.m]) are permutation equivalent if [M.sub.O'] = P[M.sub.O][P.sup.T] holds for some
permutation matrix P.
Then we have to reorder equations [PHI] := [[[[phi].sub.1] [[phi].sub.2]].sup.T] with respect to the row degrees starting from the lowest that can be done by means of multiplication by the
permutation matrix