相关论文: New Optimal $Z$-Complementary Code Sets from Matri…
In recent decades, High Performance Computing (HPC) has undergone significant enhancements, particularly in the realm of hardware platforms, aimed at delivering increased processing power while keeping power consumption within reasonable…
In this paper, an algorithm for construction of multiple sets of two dimensional (2D) or matrix unipolar (optical) orthogonal codes has been proposed. Representations of these 2D codes in difference of positions representation (DoPR) have…
We introduce the concept of Almost-Companion Matrix (ACM) by relaxing the non-derogatory property of the standard Companion Matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Spatial modulation (SM) is a new paradigm of multiple-input multiple-output (MIMO) systems, in which only one antenna at the transmitter is activated during each symbol period. Recently, it is observed that SM training sequences derived…
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank numerical ranges for a generic unitary…
A mathematical topology with matrix is a natural representation of a coding relational structure that is found in many fields of the world. Matrices are very important in computation of real applications, s ce matrices are easy saved in…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
We introduce the Z-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the Z-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion,…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network, which restricts…
The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
Copositive and completely positive matrices play an increasingly important role in Applied Mathematics, namely as a key concept for approximating NP-hard optimization problems. The cone of copositive matrices of a given order and the cone…
For a finite $\mathbb{Z}$-algebra $R$, i.e., for a $\mathbb{Z}$-algebra which is a finitely generated $\mathbb{Z}$-module, we assume that $R$ is explicitly given by a system of $\mathbb{Z}$-module generators $G$, its relation module ${\rm…
We consider polynomial codes for private distributed matrix multiplication (PDMM/SDMM). Existing codes for PDMM are either specialized for the outer product partitioning (OPP), or inner product partitioning (IPP), or are valid for the more…
Conventional Neural Networks can approximate simple arithmetic operations, but fail to generalize beyond the range of numbers that were seen during training. Neural Arithmetic Units aim to overcome this difficulty, but current arithmetic…
The unitarity of the lepton mixing matrix is a critical assumption underlying the standard neutrino-mixing paradigm. However, many models seeking to explain the as-yet-unknown origin of neutrino masses predict deviations from unitarity in…
Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence…