Related papers: Zeta Functions for Tensor Codes

The theory of Selberg zeta functions is generalized to higher rank spaces. Applications towards analytic torsion numbers are given.

This paper presents an algorithm for decoding homogeneous interleaved codes of high interleaving order in the rank metric. The new decoder is an adaption of the Hamming-metric decoder by Metzner and Kapturowski (1990) and guarantees to…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they are at most three-weight codes and they are suitable for applications…

This paper discuss a new class of functional equations by using both Poisson summation formula and Jacobi type theta a function. The class of Riemann type functional equations are derived from self-reciprocal probability density functions.…

We study meromorphic extensions of distance and tube zeta functions, as well as of geometric zeta functions of fractal strings. The distance zeta function $\zeta_A(s):=\int_{A_\delta} d(x,A)^{s-N}\mathrm{d}x$, where $\delta>0$ is fixed and…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

We give a new and short proof of the Mallows-Sloane upper bound for self-dual codes. We formulate a version of Greene's theorem for normalized weight enumerators. We relate normalized rank-generating polynomials to two-variable zeta…

Detailed notes on the functions included in the DMRjulia library are included here. This discussion of how to program functions for a tensor network library are intended to be a supplement to the other documentation dedicated to explaining…

Given a projective variety X defined over a finite field, the zeta function of divisors attempts to count all irreducible, codimension one subvarieties of X, each measured by their projective degree. When the dimension of X is greater than…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

In this paper, based on the theory of defining sets, a class of four-weight or five-weight linear codes over Fp is constructed. The complete weight enumerators of the linear codes are determined by means of Weil sums. In some case, there is…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…

In this paper, by introducing a new operation in the vector space of Laurent series, the author derived explicit series for the values of $\zeta$-funtion at positive integers, where $\zeta$ denotes the Riemann zeta function. The values of…

The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…

In problems involving approximation, completion, denoising, dimension reduction, estimation, interpolation, modeling, order reduction, regression, etc, we argue that the near-universal practice of assuming that a function, matrix, or tensor…