An enhanced Ultra Wideband (UWB) signaling scheme that employs PSWF (Prolate Spheroidal Wave Functions)-based orthogonal chip pulses and ternary complementary code sets is proposed for Direct-Sequence (DS) UWB systems...
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An enhanced Ultra Wideband (UWB) signaling scheme that employs PSWF (Prolate Spheroidal Wave Functions)-based orthogonal chip pulses and ternary complementary code sets is proposed for Direct-Sequence (DS) UWB systems. Every information bit of each user is modulated and transmitted over a set of parallel sequences of PSWF-based orthogonal chip pulses and are further assigned to a ternary complementary code set with additional zero padding if necessary: Moreover, the ternary complementary code sets are generated to be mutually orthogonal and assigned to any pair of multiple users. Hence, the mitigation of multipath interference as well as multiple user interference (MUl) can be expected. Furthermore, the ternary code length can be greatly shortened by taking advantage of pulse and code orthogonality. Thus, the proposed transmission scheme is especially suitable for high data rate DS-UWB systems that offer very high flexibility.
An enhanced Ultra Wideband (UWB) signaling scheme employing PSWF (Prolate Spheroidal Wave Functions)based orthogonal chip pulses and ternary complementary code sets is proposed for Direct-Sequence (DS) UWB systems. Ev...
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ISBN:
(纸本)9781424400850
An enhanced Ultra Wideband (UWB) signaling scheme employing PSWF (Prolate Spheroidal Wave Functions)based orthogonal chip pulses and ternary complementary code sets is proposed for Direct-Sequence (DS) UWB systems. Every information bit of each user is modulated and transmitted over a set of parallel sequences of PSWF-based orthogonal chip pulses and are further assigned to a ternary complementary code set with additional zero padding if necessary. Moreover, the ternary complementary code sets are generated to be mutually orthogonal and assigned to any pair of multiple users. Hence, the mitigation of multipath interference as well as Multiple User Interference (MUI) can be expected. Furthermore, the ternary code length can be possibly designed to be much shorter by taking advantage of the pulse and code orthogonality. Thus, the proposed transmission scheme is especially suitable for high data rate DS-UWB systems for achieving much more flexibilities.
A weighing matrix W of order n = p(m+1)-1/p-1 and weight p(m) is constructed and shown that the rows of W and -W together form optimal constant weight ternary codes of length n, weight p(m) and minimum distance p(m-1)...
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A weighing matrix W of order n = p(m+1)-1/p-1 and weight p(m) is constructed and shown that the rows of W and -W together form optimal constant weight ternary codes of length n, weight p(m) and minimum distance p(m-1) (p+3/2) for each odd prime power p and integer m >= 1 and thus A(3) (p(m+1)-1/p - 1, p(m-1)(p + 3/2), p(m)) = 2(p(m+1)-1/p - 1).
Shimada and Zhang studied the existence of polarizations on some super-singular K3 surfaces by reducing the existence of the polarizations to that of ternary [12, 5] codes satisfying certain conditions. In this note, ...
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Shimada and Zhang studied the existence of polarizations on some super-singular K3 surfaces by reducing the existence of the polarizations to that of ternary [12, 5] codes satisfying certain conditions. In this note, we give a classification of ternary [12, 5] codes satisfying the conditions. To do this, ternary [10, 5] codes are classified for minimum weights 3 and 4.
Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic ***,most of them rely on the resonant structural components,and thus are frequency...
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Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic ***,most of them rely on the resonant structural components,and thus are frequency-dependent and ***,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic *** on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are ***,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first ***,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative ***,the wave functions with detailed microstructures are numerically verified.
Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. The objective of this paper is to present ...
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Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. The objective of this paper is to present a family of optimal ternary cyclic codes from the Niho-type exponent. Specifically, for an odd integer m and a positive integer r with 4r 1(mod m), a family of cyclic codes C-(u,C- v) of length 3(m) - 1 over GF(3) with two nonzeros beta(u) and beta(v) is studied, where beta is a generator of GF(3(m))*, u = (3(m) + 1)/2 and v = 3(r) + 2 is the ternary Niho-type exponent. The parameters of this family of cyclic codes are determined. It turns out that C-(u,C- v) is optimal with respect to the Sphere Packing bound if 9 (sic) m and otherwise almost optimal. Thanks to a recent proof of the Dobbertin-Helleseth-Kumar-Martin conjecture by Katz and Langevin, the dual of this family of cyclic codes is shown to have at most five nonzero weights. (C) 2018 Elsevier Inc. All rights reserved.
A ternary self-dual code can be constructed from a Hadamard matrix of order congruent to 8 modulo 12. In this paper, we show that the Paley-Hadamard matrix is the only Hadamard matrix of order 32 which gives an extrem...
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A ternary self-dual code can be constructed from a Hadamard matrix of order congruent to 8 modulo 12. In this paper, we show that the Paley-Hadamard matrix is the only Hadamard matrix of order 32 which gives an extremal self-dual code of length 64. This gives a coding theoretic characterization of the Paley-Hadamard matrix of order 32.
In this paper, we investigate the covering radius of ternary extremal self-dual codes. The covering radii of all ternary extremal self-dual codes of lengths up to 20 were previously known. The complete coset weight di...
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In this paper, we investigate the covering radius of ternary extremal self-dual codes. The covering radii of all ternary extremal self-dual codes of lengths up to 20 were previously known. The complete coset weight distributions of the two inequivalent extremal self-dual codes of length 24 are determined. As a consequence, it is shown that every extremal ternary self-dual code of length up to 24 has covering radius which meets the Delsarte bound. The first example of a ternary extremal self-dual code with covering radius which does not meet the Delsarte bound is also found. It is worth mentioning that the found code is of length 32.
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we sett...
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Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem about a class of optimal ternary cyclic codes which was proposed by Ding and Helleseth [5]. Let C-(1,C-e) be a cyclic code of length 3(m) - 1 over GF(3) with two nonzeros alpha and alpha(e), where m and e are given integers, and alpha is a generator of GF(3(m))*. It is shown that C-(1,C-e) is optimal with parameters [3(m) - 1, 3(m)-1-2m, 4] if one of the following conditions is met. 1) m equivalent to 0(mod 4), m >= 4, and e = 3(m/2) + 5.2) m equivalent to 2(mod 4), m >= 6, and e = 3(m+2/2) + 5. (C) 2019 Published by Elsevier Inc.
It is proved that ternary codes with parameters [15,8,6], [15,9,5], [16,6,8], and [16,7,7] do not exist. This result solves the problem of finding optimal ternary linear codes of length at most 21. A table is given, s...
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It is proved that ternary codes with parameters [15,8,6], [15,9,5], [16,6,8], and [16,7,7] do not exist. This result solves the problem of finding optimal ternary linear codes of length at most 21. A table is given, showing the exact value of d(3)(n, k) for n less than or equal to 21 with the earliest references.
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