English

Probabilistic verification algorithm for linear codes

Information Theory 2026-01-06 v1 math.IT

Abstract

In this paper, we propose a probabilistic algorithm suitable for any linear code CC to determine whether a given vector x\mathbf{x} belongs to C C. The algorithm achieves O(nlogn)O(n\log n) time complexity, O(n2) O(n^2) space complexity and with an error probability less than 1/poly(n)1/\mathrm{poly}(n) in the asymptotic sense.

Keywords

Cite

@article{arxiv.2601.01372,
  title  = {Probabilistic verification algorithm for linear codes},
  author = {Mingchao Li and Jiyou Li},
  journal= {arXiv preprint arXiv:2601.01372},
  year   = {2026}
}