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Sonlu cisimler üzerindeki x^k-cx-d polinomlarının iki uygulaması üzerine ve daha fazlası
Date
2023-1-11
Author
İrimağzı, Canberk
Özbudak, Ferruh
Metadata
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For integers k∈[2,q−2] coprime to q−1 , we first bound the number of zeroes of the family of polynomials xk−cx−d∈Fq[x] where q=2n such that q−1 is a prime or q=3n such that (q−1)/2 is a prime. This gives us bounds on cross-correlation of a subfamily of Golomb Costas arrays. Next, we show that the zero set of xk−cx−d over Fq is a planar almost difference set in F∗q and hence for some set of pairs (c, d), they produce optical orthogonal codes with λ=1 . More generally, we give an algorithm to produce optical orthogonal codes (OOCs) from P(x)=xℓ1+cℓ2xℓ2+cℓ2−1xℓ2−1+⋯+c1x∈Fq[x] where interestingly ℓ1≫ℓ2 . We focus on the case ℓ2∈{2,3} and provide examples of (q−1,w,λ) -OOCs with λ∈{2,3} .
Subject Keywords
Finite Fields
,
Golomb Costas Permutations
,
Almost Difference Families
,
Optical Orthogonal Codes
,
Radar
,
Sonar
,
Optical CDMA
URI
https://doi.org/10.1007/978-3-031-22944-2_2
https://books.google.com.tr/books?hl=en&lr=&id=wd2mEAAAQBAJ&oi=fnd&pg=PA14&ots=mTv1cDMzpU&sig=EzqwShbQ0bXSFOtNjB8nT7mBIY0&redir_esc=y#v=onepage&q&f=false
Relation
Sonlu Cisimlerin Aritmetiği
Collections
Department of Mathematics, Book / Book chapter
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C. İrimağzı and F. Özbudak,
Sonlu cisimler üzerindeki x^k-cx-d polinomlarının iki uygulaması üzerine ve daha fazlası
. 2023, p. 32.