相关论文: New Optimal $Z$-Complementary Code Sets from Matri…

Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the…

Z-complementary code set (ZCCS), an extension of perfect complementary codes (CCs), refers to a set of two-dimensional matrices having zero correlation zone properties. ZCCS can be used in various multi-channel systems to support, for…

In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…

A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.

A new method to construct $q$-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size $N$ is proposed by using desired para-unitary (PU) matrices. The concept of seed PU matrices is introduced and a systematic…

We propose new constructions for a two-dimensional ($2$D) perfect array, complete complementary code (CCC), and multiple CCCs as an optimal symmetrical $Z$-complementary code set (ZCCS). We propose a method to generate a two-dimensional…

Cryptographic schemes like Fully Homomorphic Encryption (FHE) and Zero-Knowledge Proofs (ZKPs), while offering powerful privacy-preserving capabilities, are often hindered by their computational complexity. Polynomial multiplication, a core…

We extend the paraunitary (PU) theory for complementary pairs to comple- mentary sets and complete complementary codes (CCC) by proposing a new PU construction. A special, but very important case of complementary sets (and CC- C), based on…

Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…

Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasi-asynchronous environments. In this letter, we propose three new…

In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction…

The emergence of new, off-path smart network cards (SmartNICs), known generally as Data Processing Units (DPU), has opened a wide range of research opportunities. Of particular interest is the use of these and related devices in tandem with…

Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…

This whitepaper proposes the design and adoption of a new generation of Tensor Processing Unit which has the performance of Google's TPU, yet performs operations on wide precision data. The new generation TPU is made possible by…

One objective of this paper is to propose a novel class of sequence pairs, called "Quasi-orthogonal Z-complementary pairs (QOZCPs)", each depicting Z-complementary property for their aperiodic auto-correlation sums and also have a zero…

In this work, we consider complementary lattice arrays in order to enable a broader range of designs for coded aperture imaging systems. We provide a general framework and methods that generate richer and more flexible designs than existing…

Orthogonal and quasi-orthogonal matrices have a long history of use in digital image processing, digital and wireless communications, cryptography and many other areas of computer science and coding theory. The practical benefits of using…

In this paper we present a method to design paraunitary polyphase matrices of critically sampled rational filter banks. The method is based on (P,Q) shift-invariant systems, and so any kind of rational splitting of the frequency spectrum…

We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…

We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an $N \times N$…