Related papers: A Database of $\mathbb{Z}_4$ Codes
This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over Fq2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given…
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so…
Strongly lensed quadruply imaged quasars (quads) are extraordinary objects. They are very rare in the sky -- only a few tens are known to date -- and yet they provide unique information about a wide range of topics, including the expansion…
We consider private polynomial computation (PPC) over noncolluding coded databases. In such a setting a user wishes to compute a multivariate polynomial of degree at most $g$ over $f$ variables (or messages) stored in multiple databases…
Generative retrieval employs sequence models for conditional generation of document IDs based on a query (DSI (Tay et al., 2022); NCI (Wang et al., 2022); inter alia). While this has led to improved performance in zero-shot retrieval, it is…
Batch codes are a type of codes specifically designed for coded distributed storage systems and private information retrieval protocols. These codes have got much attention in recent years due to their ability to enable efficient and secure…
The biggest challenge when using DNA as a storage medium is maintaining its stability. The relative occurrence of Guanine (G) and Cytosine (C) is essential for the longevity of DNA. In addition to that, reverse complementary base pairs…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new…
In this paper, we describe a new type of DNA codes over two noncommutative rings $E$ and $F$ of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over $E$ and $F$. Using quasi self-duality, we can describe…
The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, data can be fitted as low-order polynomials of the 6…
Zipper codes are a framework for describing spatially-coupled product-like codes. Many well-known codes, such as staircase codes and braided block codes, are subsumed into this framework. New types of codes such as tiled diagonal and…
DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a…
There are now over 20 commercial vector database management systems (VDBMSs), all produced within the past five years. But embedding-based retrieval has been studied for over ten years, and similarity search a staggering half century and…
We Propose 22 unique Solutions to the Genetic Code. An Alternative Cracking, from the Perspective of a Mathematician.
Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a technique…
Associative division algebras are a rich source of fully diverse space-time block codes (STBCs). In this paper the systematic construction of fully diverse STBCs from nonassociative algebras is discussed. As examples, families of fully…
Effective search methods are crucial for improving the performance of deep generative models at test time. In this paper, we introduce a novel test-time search method, Neural Genetic Search (NGS), which incorporates the evolutionary…
Quaternions, split quaternions, and hybrid numbers are very well-known number systems. These number systems are used to make geometry in Euclidean and Lorentz spaces. These number systems can be obtained with the help of a quadratic form.…
Statistical language modeling techniques have successfully been applied to source code, yielding a variety of new software development tools, such as tools for code suggestion and improving readability. A major issue with these techniques…