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International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)

作者： Efanov, D. Sapozhnikov, V. Sapozhnikov, V. Emperor Alexander I St Petersburg State Transport St Petersburg Russia

ISBN: (纸本)9781509056484

This work is dedicated to concurrent error detection (CED) systems synthesis together with a complete concurrent self-checking structure based on the Boolean complement method. The authors share the view of the CED systems with a complete self-checking structure designed by the Boolean complement method and based on the constant-weight code "2-out-of-4". Within those systems logical accessories are installed for the purpose of avoiding the choice of operating vectors value which shall simplify the CED systems design process. The minimum number of operating vectors to be defined per the CED systems which should guarantee the entire variety of testing combination per the Boolean complement block as well as per the testing code "2-out-of-4".

关键词： concurrent error detection system Boolean complement constant-weight code code "2-out-of-4" structural redundancy

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Organization of Testing of Combinational Devices Based on Boolean Complement to constant-weight "1-out-of-4" code with Signal Compression

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AUTOMATIC CONTROL AND COMPUTER SCIENCES 2021年第2期55卷 113-124页

作者： Efanov, D., V Sapozhnikov, V. V. Sapozhnikov, Vl V. Russian Univ Transport Moscow 127994 Russia Emperor Alexander I St Petersburg State Transport St Petersburg 190031 Russia

A new approach to organizing testing of combinational devices is described;the approach implies initial compression of signals from working outputs of the test object to the binary four-digit vector and its subsequent transformation to the code word of the constant-weight "1-out-of-4" code. This approach allows reducing the complexity of technical implementation of the test circuit by decreasing the number of checked functions in the compression circuit. The number of testing organization variants of combinational devices is rather large, because it is possible to choose the compressed functions and the techniques for transforming each data vector to the code word of the "1-out-of-4" code. The paper shows that the new approach to organizing self-checking combinational devices allows improving the characteristics of distortion detection in data vectors in comparison with the traditional approach to organizing testing of devices by parity, even without special circuit analysis methods.

关键词： testing of combinational circuits method of Boolean complement constant-weight code "1-out-of-4" code signal compression error detection at circuit outputs

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Efficient Encoding of Binary constant-weight codes: Variable-Length Balancing Schemes a La Knuth

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第7期70卷 4731-4746页

作者： Dao, Duc Tu Kiah, Han Mao Nguyen, Tuan Thanh Nanyang Technol Univ Sch Phys & Math Sci Singapore 637371 Singapore Singapore Univ Technol & Design Sci Math & Technol Cluster Singapore 487372 Singapore

We study and propose schemes that map messages onto constant-weight codewords using variable-length prefixes. We provide polynomial-time computable formulas that estimate the average number of redundant bits incurred by our schemes. In addition to the exact formulas, we also perform an asymptotic analysis and demonstrate that our scheme uses 1/2 log(2) n + O(1) redundant bits to encode messages into length- n words with weight $(n/2)+ mu for constant mu . We also propose schemes that map messages into balanced codebooks with error-correcting capabilities. For such schemes, we provide methods to enumerate the average number of redundant bits.

关键词： Redundancy codes Encoding DNA Memory Transforms Surveys Balanced code constant-weight code constrained code encoding

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The completion of optimal cyclic quaternary codes of weight 3 and distance 3

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DESIGNS codeS AND CRYPTOGRAPHY 2022年第4期90卷 851-862页

作者： Lan, Liantao Chang, Yanxun Wang, Lidong South China Agr Univ Coll Math & Informat Guangzhou 510642 Peoples R China Beijing Jiaotong Univ Dept Math Beijing 100044 Peoples R China China Peoples Police Univ Sch Intelligence Policing Langfang 065000 Peoples R China South China Normal Univ Sch Comp Sci Guangzhou 510631 Peoples R China

A cyclic (n, d, w)(q) code is a cyclic q-ary code of length n, constant weight w and Hamming distance at least d. The function C A(q) (n, d, w) denotes the largest possible size of a cyclic (n, d, w) q code. A new construction, which is based on two (n, 2, 1) cyclic difference packings with given properties, is proposed for optimal (n, 3, 3)(4)codes. As a result, the exact value of C A(4)(n, 3, 3) is determined for n 18 (mod 24), and the spectrum of C A(4)(n, 3, 3) is then completely determined.

关键词： Optimal construction Cyclic code constant-weight code Multi-ary code

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Asymptotic Behavior and Typicality Properties of Runlength-Limited Sequences

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IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第3期68卷 1638-1650页

作者： Kovacevic, Mladen Vukobratovic, Dejan Univ Novi Sad Fac Tech Sci Novi Sad 21000 Serbia

This paper studies properties of binary runlength-limited sequences with additional constraints on their Hamming weight and/or their number of runs of identical symbols. An algebraic and a probabilistic (entropic) characterization of the exponential growth rate of the number of such sequences, i.e., their information capacity, are obtained by using the methods of multivariate analytic combinatorics, and properties of the capacity as a function of its parameters are stated. The second-order term in the asymptotic expansion of the rate of these sequences is also given, and the typical values of the relevant quantities are derived. Several applications of the results are illustrated, including bounds on codes for weight-preserving and run-preserving channels (e.g., the run-preserving insertion-deletion channel), a sphere-packing bound for channels with sparse error patterns, and the asymptotics of constant-weight sub-block constrained sequences. In addition, the asymptotics of a closely related notion-q-ary sequences with fixed Manhattan weight-is briefly discussed, and an application in coding for molecular timing channels is illustrated.

关键词： codes Encoding Hamming weight Probabilistic logic Upper bound Technological innovation Synchronization Constrained code constrained sequences RLL sequences constant-weight code asymptotic rate typical sequences insertion deletion weight-preserving channel timing channel Manhattan weight analytic combinatorics

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Optimal Ternary codes With weight w and Distance 2w-2 in l1-Metric

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第11期67卷 7221-7231页

作者： Wei, Xin Chen, Tingting Zhang, Xiande Univ Sci & Technol China Sch Math Sci Hefei 230026 Peoples R China Univ Sci & Technol China Sch Cyber Secur Hefei 230026 Peoples R China

The study of constant-weight codes in l(1)-metric was motivated by the duplication-correcting problem for data storage in live DNA. It is interesting to determine the maximum size of a code given the length n, weight w, minimum distance d and the alphabet size q. In this paper, based on graph decompositions, we determine the maximum size of ternary codes with constant weight w and distance 2w - 2 for all sufficiently large length n. Previously, this was known only for a very sparse family n of density 4/w(w - 1).

关键词： DNA storage constant-weight code l(1)-metric packing graph decomposition

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Coding in a Z-Channel in Case of Many Errors

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PROBLEMS OF INFORMATION TRANSMISSION 2021年第2期57卷 129-135页

作者： Lebedev, V. S. Polyanskii, N. A. Russian Acad Sci Kharkevich Inst Informat Transmiss Problems Moscow Russia Skolkovo Inst Sci & Technol Skoltech Moscow Russia Tech Univ Munich Munich Germany

We prove that the maximum number of words in a code that corrects a fraction of 1/4+ epsilon of asymmetric errors in a Z-channel is Theta(epsilon(-3/2)) as epsilon -> 0.

关键词： Z-channel minimum distance constant-weight code

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Optimal codes With Small constant weight in l₁-Metric

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第7期67卷 4239-4254页

作者： Chen, Tingting Ma, Yiming Zhang, Xiande Univ Sci & Technol China Sch Cyber Secur Hefei 230026 Peoples R China Univ Sci & Technol China Sch Math Sci Hefei 230026 Peoples R China

Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in l(1)-metric. By using packings and group divisible designs in combinatorial design theory, we give constructions of optimal codes over non-negative integers and optimal ternary codes with l(1)-weight w <= 4 for all possible distances. In general, we derive the size of the largest ternary code with constant weight w and distance 2w - 2 for sufficiently large length n satisfying n equivalent to 1, w, -w + 2, -2w + 3 (mod w(w - 1)).

关键词： DNA storage tandem duplication error constant-weight code l(1)-metric packing

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Semidefinite Programming Bounds For constant-weight codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第1期65卷 28-38页

作者： Polak, Sven C. Univ Amsterdam Korteweg De Vries Inst Math NL-1098 XG Amsterdam Netherlands

For nonnegative integers n, d, and w, let A(n, d, w) be the maximum size of a code C subset of F-n 2 with a constant weight w and minimum distance at least d(2). We consider two semidefinite programs based on quadruples of code words that yield several new upper bounds on A(n, d, w). The new upper bounds imply that A(22, 8, 10) = 616 and A(22, 8, 11) = 672. Lower bounds on A(22, 8, 10) and A(22, 8, 11) are obtained from the (n, d) = (22, 7) shortened Golay code of size 2048. It can be concluded that the shortened Golay code is a union of constant-weight w codes of sizes A(22, 8, w).

关键词： constant-weight code upper bounds semidefinite programming Delsarte Golay

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Constructions of cyclic quaternary constant-weight codes of weight three and distance four

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DESIGNS codeS AND CRYPTOGRAPHY 2018年第5期86卷 1063-1083页

作者： Lan, Liantao Chang, Yanxun Wang, Lidong Beijing Jiaotong Univ Inst Math Beijing 100044 Peoples R China Chinese Peoples Armed Police Force Acad Basic Subject Applicat & Dev Res Ctr Langfang 065000 Peoples R China

A cyclic code is a cyclic q-ary code of length n, constant-weight w and minimum distance d. A cyclic code with the largest possible number of codewords is said to be optimal. Optimal nonbinary cyclic codes were first studied in our recent paper (Lan et al. in IEEE Trans Inf Theory 62(11):6328-6341, 2016). In this paper, we continue to discuss the constructions of optimal cyclic codes. We establish the connection between cyclic codes and mutually orbit-disjoint cyclic (n, 3, 1) difference packings (briefly (n, 3, 1)-CDPs). For the case of , we construct three mutually orbit-disjoint (n, 3, 1)-CDPs by constructing a pair of strongly orbit-disjoint (n, 3, 1)-CDPs, which are obtained from Skolem-type sequences. As a consequence, we completely determine the number of codewords of an optimal cyclic code.

关键词： constant-weight code Cyclic Optimal Cyclic difference packing Orbit-disjoint

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