Probabilistic verification algorithm for linear codes
Abstract
In this paper, we propose a probabilistic algorithm suitable for any linear code $C$ to determine whether a given vector $\mathbf{x}$ belongs to $ C$. The algorithm achieves $O(n\log n)$ time complexity, $ O(n^2)$ space complexity and with an error probability less than $1/\mathrm{poly}(n)$ in the asymptotic sense.
Fields of Study & Subjects
Coding theory and cryptography
Polynomial and algebraic computation
Error Correcting Code Techniques
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 4 January 2026
- Document type
- Preprint