The uncertainty principle over finite fields
نویسندگان
چکیده
In this paper we study the uncertainty principle (UP) connecting a function over finite field and its Mattson-Solomon polynomial, which is kind of Fourier transform in positive characteristic. Three versions UP fields are studied, connection with asymptotic theory cyclic codes. We first show that no satisfies strong version UP, introduced recently by Evra, Kowalsky, Lubotzky, 2017. A refinement weak given, using Plotkin bound. naive version, direct analogue Donoho-Stark bound complex numbers, proved BCH It enough to there exist sequences codes length n, arbitrary rate, minimum distance Ω(nα) for all 0<α<1/2. Finally, Ramsey Theory pointed out.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2022
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2021.112670