arXiv subjects

Andrew Tirkel

Publications and source records attributed to Andrew Tirkel.

4 recordsLinked to original sources

arXiv2021

Correlation, Linear Complexity, Maximum order Complexity on Families of binary Sequences

Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of order $k$ and another two pseudorandom measures: the $N$th linear complexity and the $N$th maximum order complexity. We simplify and improve several state-of-the-art lower bounds for these two measures using the Hamming bound as well as weaker bounds derived from it.

cs.IT↗

arXiv2018

On the linear complexity for multidimensional sequences

In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and $k$-error linear complexity of multidimensional periodic sequences.

math.NT↗

arXiv2014

Array Orthogonality in Higher Dimensions

We generalize the array orthogonality property for perfect autocorrelation sequences to $n$-dimensional arrays. The generalized array orthogonality property is used to derive a number of $n$-dimensional perfect array constructions.

cs.IT↗

arXiv2012

Secure CDMA Sequences

Single sequences like Legendre have high linear complexity. Known CDMA families of sequences all have low complexities. We present a new method of constructing CDMA sequence sets with the complexity of the Legendre from new frequency hop patterns, and compare them with known sequences. These are the first families whose normalized linear complexities do not asymptote to 0, verified for lengths up to 6x108. The new constructions in array format are also useful in watermarking images. We present a conjecture regarding the recursion polynomials. We also have a method to reverse the process, and from small Kasami/No-Kumar sequences we obtain a new family of 2n doubly periodic (2n+1)x(2n-1) frequency hop patterns with correlation 2.

cs.CR↗