On de Bruijn Arrays Codes, Part I: Nonlinear Codes
<|reference_start|>On de Bruijn Arrays Codes, Part I: Nonlinear Codes: A de Bruijn arrays code is a set of $r \times s$ binary doubly-periodic arrays such that each binary $n \times m$ 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 arrays are given. Several direct constructions and recursive constructions for such arrays are given. A framework for a theory of two-dimensional feedback shift register which is akin to (one-dimensional) feedback shift registers is suggested.<|reference_end|>
@article{etzion2024on,
    title={On de Bruijn Arrays Codes, Part I: Nonlinear Codes},
    author={Tuvi Etzion},
    journal={arXiv preprint arXiv:2407.18122},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.18122},
    primaryClass={cs.IT math.IT}
}