For (n,q)=p(s), where p=ch(F-q), s greater than or equal to 1, V a q(m)-ary repeated-root cyclic code of length n with generator polynomial g(x), we give a partial answer about whether the q-ary image of V is cyclic o...
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For (n,q)=p(s), where p=ch(F-q), s greater than or equal to 1, V a q(m)-ary repeated-root cyclic code of length n with generator polynomial g(x), we give a partial answer about whether the q-ary image of V is cyclic or not with respect to a certain basis for F(q)m over F-q.
Server log data offers a comprehensive record of system operations, making the analysis of this data via algorithms for autonomous fault diagnosis a critical research area. At present, two primary methods of automatic...
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ISBN:
(纸本)9798350333398
Server log data offers a comprehensive record of system operations, making the analysis of this data via algorithms for autonomous fault diagnosis a critical research area. At present, two primary methods of automatic fault diagnosis prevail: traditional machine learning algorithms, such as random forests, which can efficiently and accurately deliver fault diagnosis results after manual feature extraction;and deep neural network algorithms, which can execute end-to-end fault diagnosis with large data sets and yield superior outcomes compared to the former method. However, both techniques exhibit a significant shortcoming: log files constitute time-series data, but machine learning algorithms struggle to effectively capture sequence information. Conversely, deep learning algorithms based on recurrent neural networks can grasp sequence information but lack a thorough comprehension of the system, rendering their implementation relatively demanding, as it necessitates a considerable volume of labeled *** this paper, we put forth a groundbreaking solution that amalgamates the strengths of both algorithms. We employ the chi-square test algorithm to extract features via machine learning algorithms and subsequently incorporate an attention mechanism layer into the neural network. This layer modifies the attention mechanism parameters using the chi-square test output. Moreover, we integrate cyclic codes into the neural network's word embedding, a technique that has proven highly effective in communication channel coding. We introduce the utilization of Hamming distance to quantify the disparities among various data, thereby facilitating rapid data comprehension by the neural network. Our proposed algorithm has been corroborated using a publicly accessible dataset and demonstrated a 2 percent enhancement in the F1 score.
Based on a sufficient condition proposed by Hollmann and Xiang for constructing triple-error-correcting codes, the minimum distance of a binary cyclic code C-1,C-3,C-13 with three zeros alpha, alpha(3), and alpha(13) ...
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Based on a sufficient condition proposed by Hollmann and Xiang for constructing triple-error-correcting codes, the minimum distance of a binary cyclic code C-1,C-3,C-13 with three zeros alpha, alpha(3), and alpha(13) of length 2(m) - 1 and the weight divisibility of its dual code are studied, where m >= 5 is odd and a is a primitive element of the finite field F-2m. The code C-1,C-3,C-13 is proven to have the same weight distribution as the binary triple-error-correcting primitive BCH code C-1,C-3,C-5 of the same length. (C) 2011 Elsevier Inc. All rights reserved.
We apply relations of n-dimensional Kloosterman sums to exponential sums over finite fields to count the number of low-weight codewords in a cyclic code with two zeros. As a corollary we obtain a new proof for a resul...
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We apply relations of n-dimensional Kloosterman sums to exponential sums over finite fields to count the number of low-weight codewords in a cyclic code with two zeros. As a corollary we obtain a new proof for a result of Carlitz which relates one- and two-dimensional Kloosterman sums. In addition, we count some power sums of Kloosterman sums over certain subfields. (c) 2006 Elsevier Inc. All rights reserved.
Let C be a simple-root cyclic code and let G be the subgroup of the automorphism group of C generated by the cyclic shift of C and the scalar multiplications of C. In this paper, we find an explicit formula for the nu...
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Let C be a simple-root cyclic code and let G be the subgroup of the automorphism group of C generated by the cyclic shift of C and the scalar multiplications of C. In this paper, we find an explicit formula for the number of orbits of G on C \ cyclic code. Consequently, an explicit upper bound on the number of non-zero weights of C is immediately derived and a necessary and sufficient condition for codes meeting the bound is exhibited. Several reducible and irreducible cyclic codes meeting the bound are presented, revealing that our bound is tight. In particular, we find that some infinite families of irreducible cyclic codes constructed in (Ding, 2009) meet our bound;we then conclude that such known codes enjoy an additional property that any two codewords with the same weight belong to the same G-orbit, a fact that may not have been known before. Our main result improves and generalizes some of the results in (Shi et al., 2019).
We discovered that a (148, 32) binary cyclic code generated by the product of an irreducible polynomial of degree 28 with exponent 145 and the polynomial x(4)+x(3)+x(2)+x+1 has a minimum distance of 44.
We discovered that a (148, 32) binary cyclic code generated by the product of an irreducible polynomial of degree 28 with exponent 145 and the polynomial x(4)+x(3)+x(2)+x+1 has a minimum distance of 44.
In this correspondence, we give the moments of a Kloosterman sum over F-q in terms of the frequencies of weights in the binary Zetterberg code of length q + 1, which are known by the work of Schoof and van der Vlugt. ...
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In this correspondence, we give the moments of a Kloosterman sum over F-q in terms of the frequencies of weights in the binary Zetterberg code of length q + 1, which are known by the work of Schoof and van der Vlugt. The method is illustrated by giving explicit formulae for the moments up to the tenth moment. As a corollary the weight distribution of a Zetterberg-type binary cyclic code is obtained.
For (n, q) = 1 V a q(m)-ary cyclic code of length n and with generator polynomial g(x), we show that there exists a basis for F-qm Over F-q with respect to which the q-ary image of V is cyclic, if and only if: i) g(x)...
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For (n, q) = 1 V a q(m)-ary cyclic code of length n and with generator polynomial g(x), we show that there exists a basis for F-qm Over F-q with respect to which the q-ary image of V is cyclic, if and only if: i) g(x) is over F-q;or ii) g(x) = g(0)(x)(x - gamma(-q mu)), g(0)(x) is over F-q, F-q not equal F-qk = F-q(gamma) subset of F-qm, mu an integer module k, and w(m) - gamma has a divisor over F-qk of degree e = m/k;or iii) g(x) = g(0)(x) Pi(mu is an element of S)(x - y(-q mu)), g(0)(x) is over F-q, F-q not equal F-qk = F-q(gamma) subset of F-qm, S a set of integers modulo k of cardinality k - 1 and w(m) - gamma has a divisor over F-qk of degree e = m/k. In all of the above cases, we determine all of the bases with respect to which the q-ary image of V is cyclic.
We present an alternative proof of a result of Zeng-Shan-Hu that shows that the cyclic code with three zeros alpha, alpha(3), alpha(13) has the same weight distribution as the 3-error-correcting BCH code. Our proof us...
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We present an alternative proof of a result of Zeng-Shan-Hu that shows that the cyclic code with three zeros alpha, alpha(3), alpha(13) has the same weight distribution as the 3-error-correcting BCH code. Our proof uses the theory of algebraic curves over finite fields, and combines results that are already in the literature. This method is applicable in other cases too. (C) 2011 Elsevier Inc. All rights reserved.
This paper presents an overview of the implementation of a difference-set cyclic code (1057,813,34). It is easy to achieve coding and decoding circuits. The decoding lays on the analysis of the composite remainder R(c...
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This paper presents an overview of the implementation of a difference-set cyclic code (1057,813,34). It is easy to achieve coding and decoding circuits. The decoding lays on the analysis of the composite remainder R(c)(x) and the use of a decoding matrix of 33 Boolean equations. The error-correcting algorithm has been improved, so the difference-set cyclic code (1057,813,34) can collect up to 26 random errors instead of the 16 previous random errors found by the theory. Moreover, 3 decoding algorithms have been simulated and allow the comparison of their respective efficiency. The hardware achievement is quite easy because the necessary logical elements such as shift delay registers, positive-and gates, positive-or gates, positive-exclusive-or gates exist as a set of libraries.
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