Related papers: On a Class of Almost Difference Sets Constructed b…
Pseudo-random arrays and perfect maps are the two-dimensional analogs of M-sequences and de Bruijn sequences, respectively. We modify the definitions to be applied to codes. These codes are also the two-dimensional analogs of certain…
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…
The notion off-ideals is recent and has been studied in the papers[1] [2], [5], [10], [11], [12], [13], [14] and [15]. In this paper, we have generalized the idea off-ideals to quasi f-ideals. This extended class of ideals is much bigger…
Contrastive learning is a family of self-supervised methods where a model is trained to solve a classification task constructed from unlabeled data. It has recently emerged as one of the leading learning paradigms in the absence of labels…
Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (IEEE Trans. Inf. Theory 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed…
In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…
Given the potential difficulties in obtaining large quantities of labelled data, many works have explored the use of deep semi-supervised learning, which uses both labelled and unlabelled data to train a neural network architecture. The…
We consider a binary classification problem when the data comes from a mixture of two rotationally symmetric distributions satisfying concentration and anti-concentration properties enjoyed by log-concave distributions among others. We show…
The H\'ajek-Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon-Nikodym density for each measure with respect to the other one) or…
We shall study the existence of almost split sequences in tri-exact categories, that is, extension-closed subcategories of triangulated categories. Our results unify and extend the existence theorems for almost split sequences in abelian…
This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the…
Recent advances in semi-supervised learning (SSL) demonstrate that a combination of consistency regularization and pseudo-labeling can effectively improve image classification accuracy in the low-data regime. Compared to classification,…
In this paper, the existence of perfect and quasi-perfect splitter sets in finite abelian groups is studied, motivated by their application in coding theory for flash memory storage. For perfect splitter sets we view them as splittings of…
Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In…
Chung and Graham define quasirandom subsets of $\mathbb{Z}_n$ to be those with any one of a large collection of equivalent random-like properties. We weaken their definition and call a subset of $\mathbb{Z}_n$ $\epsilon$-balanced if its…
Sequential sensor data is generated in a wide variety of practical applications. A fundamental challenge involves learning effective classifiers for such sequential data. While deep learning has led to impressive performance gains in recent…
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…
We show that almost split sequences in the category of comodules over a coalgebra with finite-dimensional right-hand term are direct limits of almost split sequences over finite dimensional subcoalgebras. In previous work we showed that…
A more sums than differences (MSTD) set is a finite subset S of the integers such that |S+S| > |S-S|. We construct a new dense family of MSTD subsets of {0, 1, 2, ..., n-1}. Our construction gives Theta(2^n/n) MSTD sets, improving the…