相关论文: New Optimal $Z$-Complementary Code Sets from Matri…
Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal…
In this work we give an efficient construction of unitary $k$-designs using $\tilde{O}(k\cdot poly(n))$ quantum gates, as well as an efficient construction of a parallel-secure pseudorandom unitary (PRU). Both results are obtained by giving…
Hladky, Hu, and Piguet [Tilings in graphons, preprint] introduced the notions of matching and fractional vertex covers in graphons. These are counterparts to the corresponding notions in finite graphs. Combinatorial optimization studies the…
Unitary 1-matrix models are shown to be exactly equivalent to hermitian 1-matrix models coupled to 2N vectors with appropriate potentials, to all orders in the 1/N expansion. This fact allows us to use all the techniques developed and…
The explosion of artificial intelligence and machine-learning algorithms, connected to the exponential growth of the exchanged data, is driving a search for novel application-specific hardware accelerators. Among the many, the photonics…
Locating the zeros of quaternionic polynomials is a fundamental problem with significant implications across scientific and engineering disciplines, yet the noncommutative nature of quaternion multiplication makes it fundamentally more…
Define Minimum Soapy Union (MinSU) as the following optimization problem: given a $k$-tuple $(X_1, X_2,..., X_k)$ of finite integer sets, find a $k$-tuple $(t_1, t_2,..., t_k)$ of integers that minimizes the cardinality of $(X_1 + t_1) \cup…
De Bruijn tori, or perfect maps, are two-dimensional periodic arrays of letters from a finite alphabet, where each possible pattern of shape (m,n) appears exactly once in a single period. While the existence of certain de Bruijn tori, such…
Scattered polynomials of a given index over finite fields are intriguing rare objects with many connections within mathematics. Of particular interest are the exceptional ones, as defined in 2018 by the first author and Zhou, for which…
Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes.…
This paper presents the first study of Graphcore's Intelligence Processing Unit (IPU) in the context of particle physics applications. The IPU is a new type of processor optimised for machine learning. Comparisons are made for…
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…
The contributions of this paper are twofold: Firstly, we introduce a novel class of sequence pairs, called "cross Z-complementary pairs (CZCPs)", each displaying zero-correlation zone (ZCZ) properties for both their aperiodic…
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network coding and distributed storage systems. The aim of this…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
We propose a novel quaternion product unit (QPU) to represent data on 3D rotation groups. The QPU leverages quaternion algebra and the law of 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted…
The everlasting bandwidth limitations in wireless communication networks has directed the researchers' thrust toward analyzing the prospect of overloaded Code Division Multiple Access (CDMA). In this paper, we have proposed a Genetic…
Byte-Pair Encoding (BPE) is a widely used method for subword tokenization, with origins in grammar-based text compression. It is employed in a variety of language processing tasks such as machine translation or large language model (LLM)…