English

Implementation of linear maps with circulant matrices via modulo 2 rectifier circuits of bounded depth

Data Structures and Algorithms 2013-05-21 v1

Abstract

In the present note we show that for any positive integer k an arbitrary Boolean circulant matrix can be implemented via modulo 2 rectifier circuit of depth 2k-1 and complexity O(n^{1+1/k}), and also via circuit of depth 2k and complexity O(n^{1+1/k} log^{-1/k} n).

Cite

@article{arxiv.1305.4389,
  title  = {Implementation of linear maps with circulant matrices via modulo 2 rectifier circuits of bounded depth},
  author = {Igor S. Sergeev},
  journal= {arXiv preprint arXiv:1305.4389},
  year   = {2013}
}

Comments

3 pages, in English; 4 pages, in Russian

R2 v1 2026-06-22T00:18:51.150Z