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 sy...
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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".
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...
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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.
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 ...
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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.
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 constantweight w and minimum distance at least d(2). We consider two semidefinite programs based on quadrupl...
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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 constantweight 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).
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 ...
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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.
In this paper, we consider optimal q-ary cyclic constant-weight codes of length n, minimum distance d, and weight w, briefly cyclic (n, d, w) q codes. We introduce the pure and mixed difference method to present a com...
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In this paper, we consider optimal q-ary cyclic constant-weight codes of length n, minimum distance d, and weight w, briefly cyclic (n, d, w) q codes. We introduce the pure and mixed difference method to present a combinatorial description for a cyclic (n, d, w) q code and then obtain some tight upper bounds on the sizes of optimal cyclic (n, d, w) q codes. Finally, by using Skolem-type sequences, we completely determine the sizes of optimal cyclic (n, d, 3) 3 codes with minimum distance 1 <= d <= 6.
The following lower bound for binary constantweightcodes are derived by an explicit construction: A(17, 4, 5) greater than or equal to 441. The construction exploits maximal sets of bases in the four-dimensional bin...
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The following lower bound for binary constantweightcodes are derived by an explicit construction: A(17, 4, 5) greater than or equal to 441. The construction exploits maximal sets of bases in the four-dimensional binary vector space pairwise intersecting in at most two vectors.
Pairwise disjoint 3-GDDs can be used to construct some optimal constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of type g (t) u (1) and establish that its necessary conditions are also suffic...
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Pairwise disjoint 3-GDDs can be used to construct some optimal constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of type g (t) u (1) and establish that its necessary conditions are also sufficient.
We refine a lower bound on the spectrum of a binary code. We give a simple derivation of the known bound on the undetected error probability of a binary code.
We refine a lower bound on the spectrum of a binary code. We give a simple derivation of the known bound on the undetected error probability of a binary code.
A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximu...
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A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximum size of the q-ary constant-composition codes with minimum distance at least 3. This bound is asymptotically optimal and generalizes the Graham-Sloane bound for binary constant-weight codes. In addition, three construction methods of constant-composition codes are presented, and a number of optimum constant-composition codes are obtained by using these constructions.
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