کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4655035 | 1632927 | 2017 | 24 صفحه PDF | دانلود رایگان |
The problem of constructing polynomials with all coefficients 1 or −1 and large merit factor (equivalently with small L4L4 norm on the unit circle) arises naturally in complex analysis, condensed matter physics, and digital communications engineering. Most known constructions arise (sometimes in a subtle way) from difference sets, in particular from Paley and Singer difference sets. We consider the asymptotic merit factor of polynomials constructed from other difference sets, providing the first essentially new examples since 1991. In particular we prove a general theorem on the asymptotic merit factor of polynomials arising from cyclotomy, which includes results on Hall and Paley difference sets as special cases. In addition, we establish the asymptotic merit factor of polynomials derived from Gordon–Mills–Welch difference sets and Sidelnikov almost difference sets, proving two recent conjectures.
Journal: Journal of Combinatorial Theory, Series A - Volume 145, January 2017, Pages 340–363