Year: 2025
Type: preprint
Abstract: In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and decoding algorithms, making them highly desirable. A key challenge in this area is achieving rates close to the half-Singleton bound for efficient linear codes over finite fields. We improve upon previous results by constructing explicit codes over \(\mathbb{F}_{q^2}\), linear over \(\mathbb{F}_q\), with rate \(1/2 - δ- \varepsilon\) that can efficiently correct a \(δ\)-fraction of indel errors, where \(q = O(\varepsilon^{-4})\). Additionally, we construct fully linear codes over \(\mathbb{F}_q\) with rate \(1/2 - 2\sqrtδ - \varepsilon\) that can also efficiently correct \(δ\)-fraction of indels. These results significantly advance the study of linear codes for the indel model, bringing them closer to the theoretical half-Singleton bound. We also generalize the half-Singleton bound, for every code \(C \subseteq \mathbb{F}^n\) linear over \(\mathbb{E} \subset \mathbb{F}\) a subfield of $\mathbb{F}$, such that \(C\) has the ability to correct \(δ\)-fraction of indels, the rate is bounded by $(1-δ)/2$.
Source: arXiv (Cornell University)
Authors: Gross, Roee, Con, Roni, Yaakobi, Eitan
Institution: Technion – Israel Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G6720256766, G8861085386
OpenAlex ID: W7084447048
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