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Showing 1 to 20 of 20 for “"Hadamard matrices"”.
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Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups
<p>Classical Hadamard matrices are orthogonal matrices whose elements are ±1. It is well-known that error correcting codes having large minimum distance between codewords can be associated with these Hadamard matrices. Indeed, the success of early Mars deep-space probes was strongly dependent upon …
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Finding Hadamard and (epsilon,delta)-Quasi-Hadamard Matrices with Optimization Techniques
… improve these techniques, we apply them to the Hadamard Conjecture (proving that Hadamard matrices exist in dimensions divisible by 4), which is a good example to study since Hadamard matrices have interesting applications (communication theory, quantum information theory, experiment design, …
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A Survey of the Hadamard Conjecture
Hadamard matrices are defined, and their basic properties outlined. A survey of historical and recent literature follows, in which a number of existence theorems are examined and given context. Finally, a new result for Hadamard matrices over $\Z_2$ is presented and given a graph-theoretic …
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Topics in Coding Theory: 1. The A(,s)(n,d) Problem in The Plotkin Region. 2. Number of Information Symbols in a Bch Code
… such that sd > t(s - 1)n. We define Generalized Hadamard matrices, using a notion of orthogonality over a group, and show that these matrices give rise to certain A(,s)(n,d) codes. Two general constructions for A(,s)(n,d) codes, which apparently do not depend on Hadamard matrices, are given. …
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Source modulated multiplexed hyperspectral imaging: Theory, hardware and application
… encoding requires the use of multiplexing matrices with positive and negative entries. The theory of multiplexing using the Hadamard matrices is developed. Results from prior art are incorporated into a singular notational system under which the different Hadamard matrices are compared with …
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Mutually Unbiased Bases in Low Dimensions
… identify d mutually unbiased (MU) complex (d×d) Hadamard matrices, defining a complete set of d+1 MU bases. This thesis is an exploration of sets of r≤d+1 MU bases in low dimensions. We derive all inequivalent sets of MU bases in dimensions two to five confirming that in these dimensions, the …
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ΕΙΔΙΚΕΣ ΚΑΤΑΣΚΕΥΕΣ ΒΕΛΤΙΣΤΩΝ ΠΕΙΡΑΜΑΤΙΚΩΝ ΣΧΕΔΙΑΣΜΩΝ
CHAP. 1ST: HADAMARD MATRICES OF ORDER N WITH MAXIMUM EXCESS, Σ(N), ARE CONSTRUCTED FOR N=40, 44, 48, 52, 80, 84. THESE GIVE "ALMOST" D-OPTIMAL SATURATED DESIGNS WHEN THE NUMBER OF OBSERVATIONS IS = 1 MOD 4. ALGORITHMS ARE GIVEN WHICH ARE COMPUTER IMPLEMENTED. CHAP. 2ND: A NEW METHOD IS GIVEN FOR …
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Boolean complementary pairs
… spectroscopy, and in the construction of Hadamard matrices. As a result, there is significant interest in understanding their mathematical structure. However, the structure of GPs appears to be very mysterious. Ternary complementary pairs (TCPs)—a generalization of GPs—are pairs of …
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Experimental Designs and Analysis of Data for Mixtures
… incomplete blocks, Scheffe's designs and Hadamard matrices is given. Draper and Lawrence have developed more sophisticated designs using techniques worked out by Box and Draper for Minimising variance and bias errors in regression equations. A critical comparison is made between their …
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Evolution of loosely synchronized spreading codes in code-division multiple-access systems
… LS codes are {O, +1, -1} codes constructed using Hadamard matrices and Golay pairs. A variation of LS codes inserts short strings of zeros between the components of the Golay pairs to increase the number of codewords, with only limited deterioration in the correlations. These strings of zeros are …
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Sedenion extension loops and frames of hypercomplex 2[superscript n]-ons
… n-k+1-12 1-122-1 23-1&cdots; 2k-1.;In Chapter 4, Hadamard matrices are discussed. It is shown that the sign matrix of the frame multiplication in the 2n-ons under the Smith-Conway or Cayley-Dickson process is a skew Hadamard matrix. These matrices are shown to be equivalent to Kronecker products …
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Design Techniques for Efficient Sparse Regression Codes
… with an efficient in-place transform based on Hadamard matrices, which dramatically reduces the overall decoder time and memory complexity with no impact on error rate. Second, an alternative SPARC design is developed, called Modulated SPARCs. These are shown to also achieve the Shannon channel …
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Row-column factorial designs and mutually orthogonal frequency rectangles
… + α + 1 ≤ k < 2αb - α, assuming there exists a Hadamard matrix of order 4b. For strength 3 we restrict ourselves to the binary case, solving it completely when q is a power of 2. In Chapter 6, our focus is on mutually orthogonal frequency rectangles (MOFR). We use orthogonal arrays and Hadamard …
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Unique cluster expansion for reliable first-principles prediction of alloy thermodynamics and phase diagrams
… to the well-studied Walsh transformation and the Hadamard matrices, whose properties are utilized in fractional factorial design principles (also known as Design of Experiment) to evaluate reliably the variables from only a selected subset of known data. Via these concepts, we develop a systematic …