• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.125-133
• /
• 2002

Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.575-584
• /
• 1996

We investigate how the code automorphism groups can be used to study such combinatorial objects as codes, finite projective planes and Hadamard matrices. For this purpose, we write down a computer program for computing code automorphisms in PASCAL language. Then we study the combinatorial properties using those code automorphism group algorithms and the relationship between combinatorial objects and codes.

• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 2004.11a
• /
• pp.126-126
• /
• 2004

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.45 no.7
• /
• pp.17-21
• /
• 2008

As with the binary pseudo-random sequences q-ary m-sequences possess very good properties which make them useful in many applications. So we construct a class of Jacket matrices by applying additive characters of the finite field $F_q$ to entries of all shifts of q-ary m-sequence. In this paper, we generalize a method of obtaining conventional Hadamard matrices from binary PN-sequences. By this way we propose Jacket matrix construction based on q-ary M-sequences.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.47 no.7
• /
• pp.93-101
• /
• 2010

In this paper we generate Gold-sequence by using M-sequence which is made by two primitive polynomial of GF(2). Generally M-sequence is generated by linear feedback shift register code generator. Here we show that this matrix of appropriate permutation has Hadamard matrix property. This matrix proves that Gold-sequence through two M-sequence and additive matrix of one column has one of major properties of Hadamard matrix, orthogonal. and this matrix show another property that multiplication with one matrix and transpose matrix of this matrix have the result of unit matrix. Also M-sequence which is made by linear feedback shift register gets Hadamard matrix property mentioned above by adding matrices of one column and one row. And high-speed conversion is possible through L-matrix and the S-matrix.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.42 no.8 s.338
• /
• pp.1-10
• /
• 2005

In this paper, the explicit low density codes construction from the generalized permutation matrices related to algebra theory is investigated, and we design several Jacket inverse block matrices on the recursive formula and permutation matrices. The results show that the proposed scheme is a simple and fast way to obtain the low density codes, and we also Proved that the structured low density parity check (LDPC) codes, such as the $\pi-rotation$ LDPC codes are the low density Jacket inverse block matrices too.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.343-352
• /
• 2006

A real matrix A is called a sign-central matrix if for, every matrix $\tilde{A}$ with the same sign pattern as A, the convex hull of columns of $\tilde{A}$ contains the zero vector. A sign-central matrix A is called a tight sign-central matrix if the Hadamard (entrywise) product of any two columns of A contains a negative component. A real vector x = $(x_1,{\ldots},x_n)^T$ is called stable if $\|x_1\|{\leq}\|x_2\|{\leq}{\cdots}{\leq}\|x_n\|$. A tight sign-central matrix is called a $tight^*$ sign-central matrix if each of its columns is stable. In this paper, for a matrix B, we characterize those matrices C such that [B, C] is tight ($tight^*$) sign-central. We also construct the matrix C with smallest number of columns among all matrices C such that [B, C] is $tight^*$ sign-central.

• Journal of the Korean Mathematical Society
• /
• v.59 no.4
• /
• pp.789-804
• /
• 2022

Striking result of Vybíral [51] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vybíral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C^*-algebras and derive the results of Schur and Vybíral. As an application, we state C^*-algebraic version of Novak's conjecture and solve it for commutative unital C^*-algebras. We formulate Pólya-Szegő-Rudin question for the C^*-algebraic Schur product of positive matrices.

• JSTS:Journal of Semiconductor Technology and Science
• /
• v.7 no.4
• /
• pp.247-253
• /
• 2007

In this paper, a high throughput multiple transform architecture for H.264 Fidelity Range Extensions (FRExt) is proposed. New techniques are adopted which (1) regularize the $8{\times}8$ integer forward and inverse DCT transform matrices, (2) divide them into four $4{\times}4$ sub-matrices so that simple fast butterfly algorithm can be used, (3) because of the similarity of the sub-matrices, mixed butterflies are proposed that all the sub-matrices of $8{\times}8$ and matrices of $4{\times}4$ forward DCT (FDCT), inverse DCT (IDCT) and Hadamard transform can be merged together. Based on these techniques, a hardware architecture is realized which can achieve throughput of 1.488Gpixel/s when processing either $4{\times}4\;or\;8{\times}8$ transform. With such high throughput, the design can satisfy the critical requirement of the real-time multi-transform processing of High Definition (HD) applications such as High Definition DVD (HD-DVD) ($1920{\times}1080@60Hz$) in H.264/AVC FRExt. This work has been synthesized using Rohm 0.18um library. The design can work on a frequency of 93MHz and throughput of 1.488Gpixel/s with a cost of 56440 gates.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.117-123
• /
• 2003

For an n ${\times}$ n real matrix X, let ${\Phi}$(X) = X o (X$\^$-1/)$\^$T/, where o stands for the Hadamard (entrywise) product. Suppose A, B, G and D are n ${\times}$ n real nonsingular matrices, and among them there are at least one solutions to the equation (equation omitted). An equivalent condition which enable (equation omitted) become a real solution ot the equation (equation omitted), is given. As application, we get new real solutions to the matrix equation (equation omitted) by applying the results of Zhang. Yang and Cao [SIAM.J.Matrix Anal.Appl, 21(1999), pp: 642-645] and Chen [SIAM.J.Matrix Anal.Appl, 22(2001), pp:965-970]. At the same time, all solutions of the matrix equation (equation omitted) are also given.