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)...
详细信息
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).
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...
详细信息
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.
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, by inve...
详细信息
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, by investigating the solutions of certain equations over finite fields, we make progress towards three conjectures about optimal ternary cyclic codes which were proposed by Ding and Helleseth.
作者:
He, ZhiwenWen, JiejingZhejiang Univ
Sch Math Sci Hangzhou 310027 Peoples R China Shandong Univ
Key Lab Cryptol Technol & Informat Secur Minist Educ Qingdao 266237 Peoples R China Shandong Univ
Sch Cyber Sci & Technol Qingdao 266237 Peoples R China
This paper is devoted to the affine-invariant ternary codes defined by Hermitian functions. We first compute the incidence matrices of the 2-designs supported by the minimum weight codewords of these ternary codes. Th...
详细信息
This paper is devoted to the affine-invariant ternary codes defined by Hermitian functions. We first compute the incidence matrices of the 2-designs supported by the minimum weight codewords of these ternary codes. Then we show that the linear codes spanned by the rows of these incidence matrices are subcodes of the 4-th order generalized Reed-Muller codes and also hold 2-designs. Finally, we determine the dimension and develop a lower bound on the minimum distance of the ternary linear codes.
Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over F-q having large minimum weights for q is an element of{2,3}. Using the cha...
详细信息
Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over F-q having large minimum weights for q is an element of{2,3}. Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over F-q, where (q, k)is an element of{(2,4),(3,2),(3,3)}. Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over F-q, where (q, k) is an element of{(2,3),(2,4),(3,2),(3,3)}.
Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight d(2)(n, k) among all binary LCD [n, k] codes and the largest minimum weight d(...
详细信息
Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight d(2)(n, k) among all binary LCD [n, k] codes and the largest minimum weight d(3)(n, k) among all ternary LCD [n, k] codes. The largest minimum weights d(2)(n, 5) and d(3)(n,4) are partially determined. We also determine the largest minimum weights d(2)(n, n - 5), d(3)(n, n - i) for i is an element of {2, 3, 4}, and d(3)(n, k) for n is an element of {11, 12, ..., 19}. (C) 2021 Elsevier Inc. All rights reserved.
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...
详细信息
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.
Designing a multifunctional metamaterial with programmable feature has become a new trend in mechanical, acoustic, and electromagnetic research fields due to the controllability of their structural behaviors and funct...
详细信息
Designing a multifunctional metamaterial with programmable feature has become a new trend in mechanical, acoustic, and electromagnetic research fields due to the controllability of their structural behaviors and functionalities. The codable or reconfigurable structures have shown more remarkable characteristics than the traditional and conventional metamaterials to implement functional programmability. However, structural complexity and hi-tech requirement are the biggest constraints to their practical applications. This paper numerically and experimentally investigates a programmable metamaterial based on ternary foldable origami in the gigahertz-frequency regime. The proposed metamaterial provides four transformable modes corresponding to four different functions of electromagnetic reflector and frequency-selectable absorbers by programming unique ternary foldable origami coded as "0", "1", and "2" for different folding levels. Interestingly, the proposed foldable origami consists of a simple dielectric paper and a bottom conductor, while there is no conductive pattern on the top. Therefore, the proposed programmable metamaterial is extremely robust and can be extended to a multiresonance mode and origami computing.
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 ...
详细信息
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.
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, ...
详细信息
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.
暂无评论