English

Pseduo-Random and de Bruijn Array Codes

Information Theory 2024-05-14 v4 math.IT

Abstract

Pseudo-random arrays and perfect maps are the two-dimensional analogs of M-sequences and de Bruijn sequences, respectively. We modify the definitions to be applied to codes. These codes are also the two-dimensional analogs of certain factors in the de Bruijn graph. These factors are called zero factors and perfect factors in the de Bruijn graph. We apply a folding technique to construct pseudo-random array codes and examine the minimum distance of the constructed codes. The folding is applied on sequences generated from irreducible polynomials or a product of irreducible polynomials with the same degree and the same exponent. Direct and recursive constructions for de Bruijn array codes are presented and discussed.

Keywords

Cite

@article{arxiv.2311.04451,
  title  = {Pseduo-Random and de Bruijn Array Codes},
  author = {Tuvi Etzion},
  journal= {arXiv preprint arXiv:2311.04451},
  year   = {2024}
}