On de Bruijn Arrays Codes, Part I: Nonlinear Codes
Information Theory
2024-12-09 v2 math.IT
Abstract
A de Bruijn array code is a set of binary doubly-periodic arrays such that each binary matrix is contained exactly once as a window in one of the arrays. Such a set of arrays can be viewed as a two-dimensional generalization of a perfect factor in the de Bruijn graph. Necessary conditions for the existence of such codes are given. Several direct constructions and recursive constructions for such arrays are given. A framework for a theory of two-dimensional feedback shift registers which is akin to (one-dimensional) feedback shift registers is suggested in the process.
Keywords
Cite
@article{arxiv.2407.18122,
title = {On de Bruijn Arrays Codes, Part I: Nonlinear Codes},
author = {Tuvi Etzion},
journal= {arXiv preprint arXiv:2407.18122},
year = {2024}
}