Related papers: On a Class of Almost Difference Sets Constructed b…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary…
During the last two decades, many kinds of periodic sequences with good pseudo-random properties have been constructed from classical and generalized cyclotomic classes, and used as keystreams for stream ciphers and secure communications.…
A space is nearly pseudocompact if and only if $\upsilon X\backslash X$ is dense in $\beta X\backslash X$. If we denote $K=cl_{\beta X}(\upsilon X\backslash X)$, then $\delta X=X\cup(\beta X\backslash K)$ is referred by Henriksen and…
Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…
Based on cyclic simplex codes, a new construction of a family of 2-generator quasi-cyclic two-weight codes is given. New optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, good QC ternary [195, 6, 126], [208,…
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…
Contrastive learning methods enforce label distance relationships in feature space to improve representation capability for regression models. However, these methods highly depend on label information to correctly recover ordinal…
We develop almost ring theory, which is a domain of mathematics somewhere halfway between ring theory and category theory (whence the difficulty of finding appropriate MSC-class numbers). We apply this theory to valuation theory and to…
This paper provides answers to questions regarding the almost sure limiting behavior of rooted, binary tree-structured rules for regression. Examples show that questions raised by Gordon and Olshen in 1984 have negative answers. For these…
The power structure over the Grothendieck (semi)ring of complex quasi-projective varieties constructed by the authors is used to express the generating series of classes of Hilbert schemes of zero-dimensional subschemes on a smooth…
The class of good semigroups is a class of subsemigroups of $N^h$, that includes the value semigroups of rings associated to curve singularities and their blowups, and allows to study combinatorically the properties of these rings. In this…
We consider error-correction coding schemes for adversarial wiretap channels (AWTCs) in which the channel can a) read a fraction of the codeword bits up to a bound $r$ and b) flip a fraction of the bits up to a bound $p$. The channel can…
The distance-3 cyclic lowest-density MDS array code (called the C-Code) is a good candidate for RAID 6 because of its optimal storage efficiency, optimal update complexity, optimal length, and cyclic symmetry. In this paper, the underlying…
Handling imbalance in class distribution when building a classifier over tabular data has been a problem of long-standing interest. One popular approach is augmenting the training dataset with synthetically generated data. While classical…
Few-shot learning can find the latent structure information between the prior knowledge and the queried data by the similarity metric of meta-learning to construct the discriminative model for recognizing the new categories with the rare…
A set A of positive integers is called a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are…
We find new constructions of infinite families of skew Hadamard difference sets in elementary abelian groups under the assumption of the existence of cyclotomic strongly regular graphs. Our construction is based on choosing cyclotomic…
This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams,…