Related papers: Endomorphisms of Linear Block Codes
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
A general method for constructing convolutional codes from units in Laurent series over matrix rings is presented. Using group ring as matrix rings, this forms a basis for in-depth exploration of convolutional codes from group ring…
We study the rank weight hierarchy of linear codes which are stable under a linear endomorphism defined over the base field, in particular when the endomorphism is cyclic. In this last case, we give a necessary and sufficient condition for…
Artificial intelligence (AI) has revolutionized software engineering (SE) by enhancing software development efficiency. The advent of pre-trained models (PTMs) leveraging transfer learning has significantly advanced AI for SE. However,…
The data input model is a fundamental component of every quantum algorithm, as its efficiency is crucial for achieving potential speed-ups over classical methods. For quantum linear algebra tasks that utilize quantum eigenvalue or singular…
A machine learning approach is presented to accelerate the computation of block polymer morphology evolution for large domains over long timescales. The strategy exploits the separation of characteristic times between coarse-grained…
We investigate layer codes, a family of three-dimensional stabilizer codes that can achieve optimal scaling of code parameters and a polynomial energy barrier, as candidates for self-correcting quantum memories. First, we introduce two…
A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual…
Often in language and other areas of cognition, whether two components of an object are identical or not determines if it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…
Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
General error locator polynomials are polynomials able to decode any correctable syndrome for a given linear code. Such polynomials are known to exist for all cyclic codes and for a large class of linear codes. We provide some decoding…
Positional Encodings (PEs) are used to inject word-order information into transformer-based language models. While they can significantly enhance the quality of sentence representations, their specific contribution to language models is not…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
There has been a recent surge of interest in automating software engineering tasks using deep learning. This paper addresses the problem of code generation, where the goal is to generate target code given source code in a different language…
In previous work, we demonstrated how decoding of a non-binary linear code could be formulated as a linear-programming problem. In this paper, we study different polytopes for use with linear-programming decoding, and show that for many…
Large Language Models (LLMs) have made significant strides in natural language processing, and a precise understanding of the internal mechanisms driving their success is essential. In this work, we analyze the trajectories of token…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…