Related papers: Reliability on QR codes and Reed-Solomon codes
Under polynomial time reduction, the maximum likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is…
The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that…
Code explanation plays a crucial role in the software engineering domain, aiding developers in grasping code functionality efficiently. Recent work shows that the performance of LLMs for code explanation improves in a few-shot setting,…
The complexity of maximal likelihood decoding of the Reed-Solomon codes $[q-1, k]_q$ is a well known open problem. The only known result in this direction states that it is at least as hard as the discrete logarithm in some cases where the…
Cheng and Wan have related the decoding of Reed-Solomon codes to the computation of discrete logarithms over finite fields, with the aim of proving the hardness of their decoding. In this work, we experiment with solving the discrete…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly sub-optimal for distributed environments due to their high overhead…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
This paper shows that there exist Reed--Solomon (RS) codes, over \black{exponentially} large finite fields \black{in the code length}, that are combinatorially list-decodable well beyond the Johnson radius, in fact almost achieving the…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
We consider the repair problem for Reed--Solomon (RS) codes, evaluated on an $\mathbb{F}_q$-linear subspace $U\subseteq\mathbb{F}_{q^m}$ of dimension $d$, where $q$ is a prime power, $m$ is a positive integer, and $\mathbb{F}_q$ is the…
The hardness of learning a function that attains a target task relates to its input-sensitivity. For example, image classification tasks are input-insensitive as minor corruptions should not affect the classification results, whereas…
Large-scale systems with all-flash arrays have become increasingly common in many computing segments. To make such systems resilient, we can adopt erasure coding such as Reed-Solomon (RS) code as an alternative to replication because…
An alternative method for collaborative decoding of interleaved Reed-Solomon codes as well as Gabidulin codes for the case of high interleaving degree is proposed. As an example of application, simulation results are presented for a…
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We…
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for…
We describe the popular BB84 protocol and critically examine its security proof as presented by Shor and Preskill. The proof requires the use of quantum error correcting codes called the Calderbank-Shor-Steanne (CSS) quantum codes. These…
Code Large Language Models (Code LLMs) are being increasingly employed in real-life applications, so evaluating them is critical. While the conventional accuracy evaluates the performance of Code LLMs on a set of individual tasks, their…
Binary code similarity detection (BCSD) serves as a fundamental technique for various software engineering tasks, e.g., vulnerability detection and classification. Attacks against such models have therefore drawn extensive attention, aiming…
Reliability prediction is crucial for ensuring the safety and security of software systems, especially in the context of industry practices. While various metrics and measurements are employed to assess software reliability, the complexity…