Related papers: Invariants for sum-rank metric codes
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes,…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
Let $\mathrm{Sym}_q(m)$ be the space of symmetric matrices in $\mathbb{F}_q^{m\times m}$. A subspace of $\mathrm{Sym}_q(m)$ equipped with the rank distance is called a symmetric rank-metric code. In this paper we study the covering…
In recent three--loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short $S$-sums) arise. They are characterized by…
Nowadays, equivalence problems are widely used in cryptography, most notably to establish cryptosystems such as digital signatures, with MEDS, LESS, PERK as the most recent ones. However, in the context of matrix codes, only the code…
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
The weight distribution of an error correcting code is a crucial statistic in determining it's performance. One key tool for relating the weight of a code to that of it's dual is the MacWilliams Identity, first developed for the Hamming…
Matrix factorization is at the heart of many machine learning algorithms, for example, dimensionality reduction (e.g. kernel PCA) or recommender systems relying on collaborative filtering. Understanding a singular value decomposition (SVD)…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
Source code summarization involves creating brief descriptions of source code in natural language. These descriptions are a key component of software documentation such as JavaDocs. Automatic code summarization is a prized target of…
We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…
We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix…
Recht, Fazel, and Parrilo provided an analogy between rank minimization and $\ell_0$-norm minimization. Subject to the rank-restricted isometry property, nuclear norm minimization is a guaranteed algorithm for rank minimization. The…