Related papers: An Algorithm for Computing the Covering Radius of …
We present a zero-crossings counting problem that is a generalization of the Bernstein-Vazirani problem. The goal of this problem is to count the number of zero-crossings (or sign changes) in a special type of sequence S, whose definition…
We apply the coordinate-space method by Luescher and Weisz to the computation of two-loop diagrams in full QCD with Wilson fermions on the lattice. The essential ingredient is the high-precision determination of mixed fermionic-bosonic…
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
In this text we develop some aspects of Harder-Narasimhan theory, slopes, semistability and canonical filtration, in the setting of combinatorial lattices. Of noticeable importance is the Harder-Narasimhan structure associated to a Galois…
We construct trace codes over $\Z_4$ by using Boolean functions and skew sets, respectively. Their Lee weight distribution is studied by using a Galois ring version of the Walsh-Hadamard transform and exponential sums. We obtain a new…
In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…
In this paper, we study the weight spectrum of linear codes with \emph{super-linear} field size and use the probabilistic method to show that for nearly all such codes, the corresponding weight spectrum is very close to that of a maximum…
Linear codes with a few weights have wide applications in information security, data storage systems, consuming electronics and communication systems. Construction of the linear codes with a few weights and determination of their parameters…
In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code.…
Krawtchouk polynomials appear in a variety of contexts, most notably as orthogonal polynomials and in coding theory via the Krawtchouk transform. We present an operator calculus formulation of the Krawtchouk transform that is suitable for…
Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data…
Polar codes are constructed based on the reliability of sub-channels resulting from the polarization effect. However, this information-theoretic construction approach leads to a poor weight distribution. To address this issue,…
We present the general framework of \'Ecalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and calculability. We modify then \'Ecalle's…
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using…
A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation…
We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color images…
We study generalized covering radii, a fundamental property of linear codes that characterizes the trade-off between storage, latency, and access in linear data-query protocols such as PIR. We prove lower and upper bounds on the generalized…
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…