Related papers: A Method to determine Partial Weight Enumerator fo…
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
We describe an empirical approach to identify low-weight combinations of columns of the decoding matrices of a quantum circuit-level noise model, for which belief-propagation (BP) algorithms converge possibly very slowly. Focusing on the…
In this paper, we have introduced the concepts of support distribution and the support enumerator as refinements of the classical weight distribution and weight enumerator respectively, capturing coordinate level activity in linear block…
Binary Neural Networks (BiNNs), which employ single-bit precision weights, have emerged as a promising solution to reduce memory usage and power consumption while maintaining competitive performance in large-scale systems. However, training…
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial…
Mixture modeling, which considers the potential heterogeneity in data, is widely adopted for classification and clustering problems. Mixture models can be estimated using the Expectation-Maximization algorithm, which works with the complete…
The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of $t$-weight linear codes over ${\mathbb F}_{q}$ are presented with…
Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…
Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be…
Given n elements with nonnegative integer weights w1,..., wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given…
Minimum-weight perfect matching (MWPM) has been been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108,…
Image classification technology and performance based on Deep Learning have already achieved high standards. Nevertheless, many efforts have conducted to improve the stability of classification via ensembling. However, the existing ensemble…
To conduct regression analysis for data contaminated with outliers, many approaches have been proposed for simultaneous outlier detection and robust regression, so is the approach proposed in this manuscript. This new approach is called…
This paper addresses Monte Carlo algorithms for calculating the Shapley-Shubik power index in weighted majority games. First, we analyze a naive Monte Carlo algorithm and discuss the required number of samples. We then propose an efficient…
Constant-weight and constant-charge binary sequences with constrained run length of zeros are introduced. For these sequences, the weight and the charge distribution are found. Then, recurrent and direct formulas for calculating the number…
Pomset block metric is a generalization of pomset metric. In this paper, we define weight enumerator of linear block codes in pomset metric over $\mathbb{Z}_m$ and establish MacWilliams type identities for linear block codes with respect to…
Effective iterative decoding of short BCH codes faces two primary challenges: identifying an appropriate parity-check matrix and accelerating decoder convergence. To address these issues, we propose a systematic scheme to derive an…
Linear codes generated by component functions of perfect nonlinear (PN) and almost perfect nonlinear (APN) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper…