Semi Williamson Type Matrices and the W (2n; N) Conjecture
نویسندگان
چکیده
Four (1,-1, 0)-matrices of order m, X = (x ij), Y = (y ij), Z = (z ij), U = (u ij) satisfying will be called semi Williamson type matrices of order m. In this paper we prove that if there exist Williamson type matrices of order n 1 ;: :: ;n k then there exist semi Williamson type matrices of order N = Q k j=1 n rj j , where r j are non-negative integers. As an application, we obtain a W(4N;2N). Although the paper presents no new W(4n;2n) for n, odd, n < 3000, it is a step towards proving the conjecture that there exists a W(4n; 2n) for any positive integer n. This conjecture is a sub-conjecture of the Seberry conjecture 3, page 92] that W(4n;k) exist for all k = 0; 1;:: :; 4n. In addition we nd innnitely many new W(2n;n), n odd and the sum of two squares.
منابع مشابه
Some infinite classes of Williamson matrices and weighing matrices
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