2023/11/08 by Tuvi Etzion, Etzion, Tuvi
Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2311.04451
openalex publication_date 2023/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.