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Proceedings of the American Mathematical Society, 1988
Summary: A new, surprisingly simple proof is given of the finiteness of the set of matroids minor-minimally not representable over GF(3). It is, in fact, proved that every such matroid has rank or corank at most 3.
Kahn, Jeff, Seymour, Paul
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Summary: A new, surprisingly simple proof is given of the finiteness of the set of matroids minor-minimally not representable over GF(3). It is, in fact, proved that every such matroid has rank or corank at most 3.
Kahn, Jeff, Seymour, Paul
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Codesign of a Computationally Intensive Problem in GF(3)
18th IEEE/IFIP International Workshop on Rapid System Prototyping (RSP '07), 2007A reprogrammable hardware platform is used for the co-design and implementation of a computational intensive mathematical problem, namely the listing of irreducible polynomials over Galois fields of order 3 (GF(3)), The main goal is to accelerate the performance compared to an existing software implementation.
Kenneth B. Kent +2 more
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Studia Logica, 2002
For an algebra \textbf{A}, \(p_n({\mathbf A})\) denotes the number of essentially \(n\)-ary term functions over \textbf{A}. It was shown by \textit{G. Grätzer} and \textit{R. Padmanabhan} [Proc. Am. Math. Soc. 28, 75-80 (1971; Zbl 0215.34501)] that an algebra \textbf{A} is a nontrivial affine space over GF(3) if and only if \(p_n({\mathbf A})=(2^n-(-1)^
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For an algebra \textbf{A}, \(p_n({\mathbf A})\) denotes the number of essentially \(n\)-ary term functions over \textbf{A}. It was shown by \textit{G. Grätzer} and \textit{R. Padmanabhan} [Proc. Am. Math. Soc. 28, 75-80 (1971; Zbl 0215.34501)] that an algebra \textbf{A} is a nontrivial affine space over GF(3) if and only if \(p_n({\mathbf A})=(2^n-(-1)^
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Family of fast transforms over GF(3) logic
33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings., 2004New classes of recursive transforms over GF(3) have been introduced here. They are based on simple recursive equations what allows to obtain corresponding fast forward and inverse transforms and very regular butterfly diagrams. The classification is further extended into various transforms with horizontal and vertical permutations.
Bogdan J. Falkowski, Cheng Fu 0001
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SAR Tomographic Imaging Demonstration Using GF-3 Data
IGARSS 2019 - 2019 IEEE International Geoscience and Remote Sensing Symposium, 2019Synthetic aperture radar (SAR) tomography (TomoSAR) is well established for three-dimensional (3D) reconstruction in urban buildings. There are many methods usually require a large data stacks for a reliable reconstruction and very few methods to handle small data stacks.
Hongliang Lu +4 more
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Polynomial expansions over GF(3)based on fastest transformation
33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings., 2004A new fastest Linearly Independent (LI) transforms over GF(3) and its corresponding polynomial expansions have been introduced. The number of required additions and multiplications in new LI transform is advantageous when compared with ternary Reed-Muller transform, which was previously known as the most efficient transform over GF(3).
Bogdan J. Falkowski, Cheng Fu 0001
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CLASSIFICATION OF NEW LINEARLY INDEPENDENT TRANSFORMS OVER GF(3)
Journal of Circuits, Systems and Computers, 2005New classes of ternary linearly independent transforms as the bases of ternary polynomial expansions over GF(3) are introduced here. Recursive equations defining the linearly independent transforms and their corresponding butterfly diagrams are shown.
Bogdan J. Falkowski, Cheng Fu 0001
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Fastest linearly independent arithmetic transforms over GF(3)
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)., 2003In this paper, the family of fastest ternary linearly independent arithmetic transforms, which possesses forward and inverse butterfly diagrams with lowest computational complexity have been identified. This family is recursively defined and has consistent formulas relating forward and inverse transform matrices.
Bogdan J. Falkowski, Cheng Fu 0001
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Marine targets detection using GF-3 SAR data
2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2017In this letter, we present a business process flow of marine target detection using GF-3 SAR data. It includes 12 kinds of imaging modes and 3 types of polarization. The detection method for the single polarization data is a Double-Parameter Constant False Alarm Ratio (DP-CFAR) algorithm.
Peng Chen 0019 +2 more
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