Related papers: Robust Locally Testable Codes and Products of Code…
In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new soundness of the…
Designing channel codes under low-latency constraints is one of the most demanding requirements in 5G standards. However, a sharp characterization of the performance of traditional codes is available only in the large block-length limit.…
The degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…
We propose to extend property-based testing to substructural logics to overcome the current lack of reasoning tools in the field. We take the first step by implementing a property-based testing system for specifications written in the…
Modern distributed computation infrastructures are often plagued by unavailabilities such as failing or slow servers. These unavailabilities adversely affect the tail latency of computation in distributed infrastructures. The simple…
Software measurement is an essential management tool to develop robust and maintainable software systems. Software metrics can be used to control the inherent complexities in software design. To guarantee that the components of the software…
We construct the first (locally computable, approximately) locally list decodable codes with rate, efficiency, and error tolerance approaching the information theoretic limit, a core regime of interest for the complexity theoretic task of…
In this work, we present the first local-decoding algorithm for expander codes. This yields a new family of constant-rate codes that can recover from a constant fraction of errors in the codeword symbols, and where any symbol of the…
Locally repairable codes enables fast repair of node failure in a distributed storage system. The code symbols in a codeword are stored in different storage nodes, such that a disk failure can be recovered by accessing a small fraction of…
In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…
For a robust leverage diagnostic in linear regression, Rousseeuw and van Zomeren [1990] proposed using robust distance (Mahalanobis distance computed using robust estimates of location and covariance). However, a design matrix X that…
Locally recoverable codes are widely used in distributed and cloud storage systems. The objective of this paper is to present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out…
Local robustness ensures that a model classifies all inputs within an $\ell_2$-ball consistently, which precludes various forms of adversarial inputs. In this paper, we present a fast procedure for checking local robustness in feed-forward…
Fix a prime $p$ and a positive integer $R$. We study the property testing of functions $\mathbb F_p^n\to[R]$. We say that a property is testable if there exists an oblivious tester for this property with one-sided error and constant query…
Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
Reversible Primitive Permutations (RPP) are recursively defined functions designed to model Reversible Computation. We illustrate a proof, fully developed with the proof-assistant Lean, certifying that: "RPP can encode every Primitive…
In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent…
This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence…
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…