On linear complexity of binary lattices, II

Katalin Gyarmati (1) , Christian Mauduit (2) , András Sárközy (1)

1 Department of Algebra and Number Theory [Budapest]
2 I2M - Institut de Mathématiques de Marseille

The linear complexity is an important and frequently used measure of unpredictably and pseudorandomness of binary sequences. In Part I of this paper, we extended this notion to two dimensions: we defined and studied the linear complexity of binary and bit lattices. In this paper, first we will estimate the linear complexity of a truly random bit (M, N)-lattice. Next we will extend the notion of k-error linear complexity to bit lattices. Finally, we will present another alternative definition of linear complexity of bit lattices.

Mots clés: Linear complexity; Linear recursion; Two dimensions; Binary lattice; Pseudorandomness

Domaines: Théorie des nombres [math.NT]

Katalin Gyarmati, Christian Mauduit, András Sárközy. On linear complexity of binary lattices, II. Ramanujan Journal, 2014, 34 (2), pp.237-263. ⟨10.1007/s11139-013-9500-4⟩. ⟨hal-01272375⟩