首页|On skew-symmetric Toeplitz matrices over finite fields with periodicity conditions
On skew-symmetric Toeplitz matrices over finite fields with periodicity conditions
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NSTL
Elsevier
Let (a) = a(0), a(1), a(2),... be a sequence over any finite field Fwith a(0)= 0. For each positive integer n, let A(n) be the associated n x n skew-symmetric Toeplitz matrix [a(0) a(1) a(2) a(3) . . . a(n-1) - a(1) a(0) a(1) a(2) . . . a(n-2) -a(2) -a(1) a(0) a(1) . . . a(n-3) . . . . . . . . . . . . . . . -a(n-1) -a(n-2) -a(n-3)...... a(0)] If the sequence is eventually periodic but not mirrorperiodic, then the nullitysequence {nu(n)= null(A(n)) : n is an element of N} is also eventually periodic, where nu(n)= null(A(n)) is the nullity of the matrix A(n). For s a certain multiple of the period of the nullity sequence, a recursion formula produces the vectors in ker(A(n+qs)) from those in ker(A(n)), for nsufficiently large and for non-negative integers q. Published by Elsevier Inc.
NSTL
Elsevier
