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We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
Sequence alignments are used to capture patterns composed of elements representing multiple conceptual levels through the alignment of sequences that contain overlapping and variable length annotations. The alignments also determine the…
Nonlinear time-dependent partial differential equations are essential in modeling complex phenomena across diverse fields, yet they pose significant challenges due to their computational complexity, especially in higher dimensions. This…
Index Coding has received considerable attention recently motivated in part by real-world applications and in part by its connection to Network Coding. The basic setting of Index Coding encodes the problem input as an undirected graph and…
Structural probes learn a linear transformation to find how dependency trees are embedded in the hidden states of language models. This simple design may not allow for full exploitation of the structure of the encoded information. Hence, to…
In this paper, several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions are constructed based on a generic construction method. Instead of the whole space, we use the subspaces $B_+(f)$ or $B_-(f)$…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system…
Boolean cardinality constraints state that at most (at least, or exactly) $k$ out of $n$ propositional literals can be true. We propose a new class of selection networks that can be used for an efficient encoding of them. Several comparator…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
Proving capacity for networks without feedback or cooperation usually involves two fundamental random coding techniques: superposition coding and binning. Although conceptually very different, these two techniques often achieve the same…
The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Due to the increased availability of large datasets of biological sequences, the tools for sequence comparison are now relying on efficient alignment-free approaches to a greater extent. Most of the alignment-free approaches require the…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Knowledge graphs (KGs) provide information in machine interpretable form. In cases where multiple KGs are used in the same system, that information needs to be integrated. This is usually done by automated matching systems. Most of those…
Ternary and binary neural networks enable multiplication-free computation and promise multiple orders of magnitude efficiency gains over full-precision networks if implemented on specialized hardware. However, since both the parameter and…
Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…
The equivalent binary parity check matrices for the binary images of the cycle-free non-binary LDPC codes have numerous bit-level cycles. In this paper, we show how to transform these binary parity check matrices into their cycle-free…
We establish a duality result between linear index coding and Locally Repairable Codes (LRCs). Specifically, we show that a natural extension of LRCs we call Generalized Locally Repairable Codes (GLCRs) are exactly dual to linear index…