Arithmetic crosscorrelation of binary $m$-sequences with coprime periods

TL;DR

This paper determines the bounds of the arithmetic crosscorrelation between binary m-sequences with coprime periods, showing it does not exceed a specific exponential function of the smaller period.

Contribution

It provides a precise calculation of the arithmetic crosscorrelation for binary m-sequences with coprime periods, a previously unresolved problem.

Findings

The absolute value of the crosscorrelation is at most 2^{min(n1,n2)} - 1.

The result applies to sequences with coprime periods of the form 2^{n}-1.

The bounds improve understanding of sequence correlation properties in cryptography.

Abstract

The arithmetic crosscorrelation of binary $m$-sequences with coprime periods $2^{n_1}-1$ and $2^{n_2}-1$\ ($\gcd(n_1,n_2)=1$) is determined. The result shows that the absolute value of arithmetic crosscorrelation of such binary $m$-sequences is not greater than $2^{\min(n_1,n_2)}-1$.