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In this paper, we propose a new class of error-detecting codes based on quasigroups using automorphisms of the finite field 픽pn and the additive group (픽p, +). We demonstrate that these codes are effective in detecting burst errors caused by hardware damage or noisy transmission. We also explore the codes ability to detect various types of double errors, including transposition errors, twin errors, and phonetic errors. Our analysis extends beyond bit-level errors to include block-level errors. Finally, we provide a comparative analysis and demonstrate the real-world applications of our code. [ABSTRACT FROM AUTHOR]

In this paper we will analyze one linear code from the theoretical point of view. Namely, the code definition is based on linear quasigroups. In the previous work we classified the quasigroups of order 4 according to their probability of undetected errors. Now, in this paper we will conclude whether the linear quasigroups that are in the same class in this classification obtain equal number of surely detected incorrectly transmitted bits. Also, we will classify the linear quasigroups of order 4 according to the number of errors that the code surely detects when they are used for coding. At the end we will make conclusion which quasigroups of order 4 are overall best for coding having in mind both important parameters for every code for error detection: the number of errors that the code surely detects and the probability of undetected errors. [ABSTRACT FROM AUTHOR]

Let λ = λ0 + uλ1 + ⋯ + uk−1λ k−1 be a Type 1 unit in ℜk = 픽pm + u픽pm + ⋯ + uk−1픽 pm(uk = 0), where p is an odd prime, m is a positive integer and λ0,λ1,…,λk−1 ∈ 픽pm,λ0≠0,λ1≠0. In this paper, we give the complete structure of all Type 1 λ-constacyclic codes and their duals of length 8ps over the finite commutative chain ring ℜk in terms of their generator polynomials. Using this structure, we determine the Hamming distance and the Rosenbloom–Tsfasman (RT) distance of all Type 1 λ-constacyclic codes. For pm ≡ 1(mod 4) and a unit λ ∈ ℜ2, we determine the b -symbol distances of all λ-constacyclic codes of length 8ps over ℜ2, where b ≤ 8. As illustrations, we provide several λ-constacyclic codes with new parameters with respect to Hamming, RT and b-symbol metrics. MDS codes are widely recognized for their optimal error-correction capability, and MDS b-symbol codes are generalization of MDS codes. We found some MDS b-symbol constacyclic codes of length 8ps over ℜ2. Additionally, for pm ≡ 1(mod 4), we provide a decoding algorithm for Type 1 constacyclic codes of length 8ps over ℜk with respect to the Hamming, RT and b-symbol metrics. [ABSTRACT FROM AUTHOR]

The problem of classifying constacyclic codes over a finite field, both the Hamming distance and the algebraic structure, is an interesting problem in algebraic coding theory. For the repeated-root constacyclic codes of length n p s over p m , where p is a prime number and p does not divide n , the problem has been solved completely for all n ≤ 6 and partially for n = 7 , 8. In this paper, we solve the problem for n = 9 and all primes p different from 3 and 1 9. In particular, we characterize the Hamming distance of all repeated-root constacyclic codes of length 9 p s over p m . As an application, we identify all optimal and near-optimal codes with respect to the Singleton bound of these types, namely, MDS, almost-MDS, and near-MDS codes. [ABSTRACT FROM AUTHOR]

Testing modern integrated circuit (IC) is challenging with introduction of System-on Chip (SOC). Enormous test pattern count is required to authenticate the IC which inflates power consumption. Henceforth, it is mandatory to incorporate power minimization techniques at circuit design phase. Optimizing test patterns is one such effective technique that curtails test power without altering circuit design. In this paper, a new test pattern reordering algorithm is proposed based on Recurrent Neural Network. Hopfield Neural Network (HNN) constitutes an optimized solution for solving traveling salesman problem (TSP). Since, test pattern reordering can be interpreted as TSP, optimized test pattern order is attained with HNN. Energy function of this algorithm falls into local minimum, so to eradicate this issue, the algorithm is modified. Test patterns are reordered with minimal hamming distance among consecutive test patterns. The proposed algorithm is implemented in ISCAS'89 Sequential Benchmark circuits. Experimental results prove that significant reduction in transition count is accomplished with proposed algorithm without compromising fault coverage. [ABSTRACT FROM AUTHOR]

Given a network G = (N , A , c) and an s − t cut [ S , S ̄ ] with the capacity β and the constant value α , an inverse minimum s − t cut problem with value constraint is to modify the vector capacity c as little as possible to make the s − t cut [ S , S ̄ ] become a minimum s − t cut with the capacity α. The distinctive feature of this problem with the inverse minimum cut problems is the addition of a constraint in which the capacity of the given cut has to equal to the preassumed value α. In this paper, we investigate the inverse minimum s − t cut problem with value constraint under the bottleneck weighted Hamming distance. We propose two strongly polynomial time algorithms based on a binary search to solve the problem. At each iteration of the first one, we solve a feasible flow problem. The second algorithm considers the problem in two cases β > α and β < α. In this algorithm, we first modify the capacity vector such that the given cut becomes a minimum s − t cut in the network and then, by preserving optimality this s − t cut, adjust it to satisfy value constraint. [ABSTRACT FROM AUTHOR]

Feature extraction and matching are the basic procedures of the so-called Visual Odometer (VO), Simultaneous Localization and Mapping (SLAM) and many other image processing algorithms. Oriented features from accelerated segment test (FAST) and rotated binary robust independent elementary features (ORB) algorithm are widely used since they are computationally faster. In this paper, we proposed a method to generate a value for a feature, the value is called signature. In the matching step, we only compute Hamming distances of descriptors with the same signatures. Hence, the matching time is shortened. Compared with the original ORB algorithm, features to be matched dropped 69.63% on TUM datasets and 85.7% on VGG datasets by adopting our strategy. In addition, the precision is above 85% on both VGG and TUM datasets. We design a customized hardware architecture for ORB feature extraction and matching based on the proposed method. The hardware structure is implemented on Xilinx ZCU102 evaluation board. The clock frequency is set to 150 MHz. Our Field Programmable Gate Arrays (FPGA) system achieves 193 fps on 1 2 8 0 × 7 2 0 images with 1984 features on average and 314 fps on 6 4 0 × 4 8 0 images with 700 features on average, which is more efficient compared to the state-of-the-art works. [ABSTRACT FROM AUTHOR]