Pseduo-Random and de Bruijn Array Codes

Tuvi Etzion

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arXiv · 2311.04451

Pseduo-Random and de Bruijn Array Codes

Tuvi Etzion

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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.

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Tuvi Etzion. 2023-11-08. Pseduo-Random and de Bruijn Array Codes. https://arxiv.org/abs/2311.04451

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