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Of the many potential hardware platforms, superconducting quantum circuits have become the leading contender for constructing a scalable quantum computing system. All current architecture designs necessitate a 2D arrangement of…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
In large-scale distributed storage systems, erasure codes are used to achieve fault tolerance in the face of node failures. Tuning code parameters to observed failure rates has been shown to significantly reduce storage cost. Such tuning of…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…
In this paper, we construct several infinite families of $q$-ary constacyclic codes over a finite field $\mathbb{F}_q$ with length $n$, dimension around $n/2$, and minimum distance at least $cn/\log_q n$ for some positive constant $c$. They…
In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a {\it junta}; i.e. a subspace code in which all codewords…
Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$,…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
The set of all subspaces of $\mathbb{F}_q^n$ is denoted by $\mathbb{P}_q(n)$. The subspace distance $d_S(X,Y) = \dim(X)+ \dim(Y) - 2\dim(X \cap Y)$ defined on $\mathbb{P}_q(n)$ turns it into a natural coding space for error correction in…
We propose to study unweighted graphs of constant distance VC-dimension as a broad generalization of many graph classes for which we can compute the diameter in truly subquadratic-time. In particular for any fixed $H$, the class of…
Many-hypercube codes, concatenated ${[[n,n-2,2]]}$ quantum error-detecting codes ($n$ is even), have recently been proposed as high-rate quantum codes suitable for fault-tolerant quantum computing. While the original many-hypercube codes…
One of the main problems in random network coding is to compute good lower and upper bounds on the achievable cardinality of the so-called subspace codes in the projective space $\mathcal{P}_q(n)$ for a given minimum distance. The…
In this paper we construct new Griesmer codes of dimension $k\geq 5$ by means of some geometric methods such as projective dual and geometric puncturing.
Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…
A geometrically local quantum code is an error correcting code situated within $\mathbb{R}^D$, where the checks only act on qubits within a fixed spatial distance. The main question is: What is the optimal dimension and distance for a…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…