相关论文: Lifting a CSS code via its handlebody realization

Formal methods for software development have made great strides in the last two decades, to the point that their application in safety-critical embedded software is an undeniable success. Their extension to non-critical software is one of…

Handwritten Text Recognition has achieved an impressive performance in public benchmarks. However, due to the high inter- and intra-class variability between handwriting styles, such recognizers need to be trained using huge volumes of…

Coded caching is a technique for achieving increased throughput in cached networks during peak hours. Placement delivery arrays (PDAs) capture both placement and delivery scheme requirements in coded caching in a single array. Lifting is a…

CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank-Shor-Steane quantum code, defined over a q-ary…

Image quantization is a crucial technique in image generation, aimed at learning a codebook that encodes an image into a discrete token sequence. Recent advancements have seen researchers exploring learning multi-modal codebook (i.e.,…

In this paper we give the generalization of lifted codes over any finite chain ring. This has been done by using the construction of finite chain rings from $p$-adic fields. Further we propose a lattice construction from linear codes over…

Graphs and recently hypergraphs have been known as an important tool for considering different properties of quantum many-body systems. In this paper, we study a mapping between an important class of quantum systems namely quantum…

In this paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum…

We introduce a twisted fiber bundle construction of quantum CSS codes over group algebras \(R=\mathbb F_2[G]\), where each base generator carries a generator-dependent \(R\)-linear fiber twist satisfying a flatness condition. This…

Recently, a new class of quantum codes based on hypermaps were proposed. These codes are obtained from embeddings of hypergraphs as opposed to surface codes which are obtained from the embeddings of graphs. It is natural to compare these…

We present a systematic method for translating fault-tolerant quantum circuits between their braiding and lattice surgery (LS) representations within the surface code. Our approach employs the ZX calculus to establish an equivalence between…

In this paper, we propose \textbf{UniCode}, a novel approach within the domain of multimodal large language models (MLLMs) that learns a unified codebook to efficiently tokenize visual, text, and potentially other types of signals. This…

Quick Response (QR) code is one of the most worldwide used two-dimensional codes.~Traditional QR codes appear as random collections of black-and-white modules that lack visual semantics and aesthetic elements, which inspires the recent…

In previous work (`Network coding meets TCP') we proposed a new protocol that interfaces network coding with TCP by means of a coding layer between TCP and IP. Unlike the usual batch-based coding schemes, the protocol uses a TCP-compatible…

Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…

In this paper, we demonstrate a direct correspondence between phase-free ZX diagrams, a graphical notation for representing and manipulating a certain class of linear maps on qubits, and Calderbank-Shor-Steane (CSS) codes, a large family of…

The aim of this paper is to present a construction of $t$-divisible designs for $t>3$, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties…

Text-to-CAD code generation is a long-horizon task that translates textual instructions into long sequences of interdependent operations. Existing methods typically decode text directly into executable code (e.g., bpy) without explicitly…

We study finite-field extensions that preserve the same support as the parity-check matrices defining a given binary CSS code. Here, an LDPC-CSS code refers to a CSS code whose parity-check matrices are orthogonal in the sense that each…

MDS codes are elegant constructions in coding theory and have mode important applications in cryptography, network coding, distributed data storage, communication systems et. In this study, a method is given which MDS codes are lifted to a…