کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895665 | 1630352 | 2018 | 32 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Existence of primitive 1-normal elements in finite fields
ترجمه فارسی عنوان
وجود عناصر ابتدایی 1 عادی در زمینه های
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
An element αâFqn is normal if B={α,αq,â¦,αqnâ1} forms a basis of Fqn as a vector space over Fq; in this case, B is a normal basis of Fqn over Fq. The notion of k-normal elements was introduced in Huczynska et al. (2013) [10]. Using the same notation as before, α is k-normal if B spans a co-dimension k subspace of Fqn. It can be shown that 1-normal elements always exist in Fqn, and Huczynska et al. (2013) [10] show that elements that are simultaneously primitive and 1-normal exist for qâ¥3 and for large enough n when gcdâ¡(n,q)=1 (we note that primitive 1-normals cannot exist when n=2). In this paper, we complete this theorem and show that primitive, 1-normal elements of Fqn over Fq exist for all prime powers q and all integers nâ¥3, thus solving Problem 6.3 from Huczynska et al. (2013) [10].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 238-269
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 238-269
نویسندگان
Lucas Reis, David Thomson,