On a conjecture of Helleseth
Yves Aubry (IML, IMATH), Philippe Langevin (IMATH)
TL;DR
This paper investigates a long-standing conjecture by Helleseth regarding zero Fourier coefficients in maximal sequences, providing new divisibility properties to advance understanding of the problem.
Contribution
It introduces new divisibility properties related to Helleseth's conjecture, offering insights into the existence of zero Fourier coefficients in maximal sequences.
Findings
Derived divisibility properties supporting the conjecture
Provided partial results towards the existence of zero Fourier coefficients
Enhanced understanding of sequence cross-correlations
Abstract
We are concern about a conjecture proposed in the middle of the seventies by Hellesseth in the framework of maximal sequences and theirs cross-correlations. The conjecture claims the existence of a zero outphase Fourier coefficient. We give some divisibility properties in this direction.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical Approximation and Integration · Approximation Theory and Sequence Spaces