کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11017685 | 1722376 | 2019 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Constructions of skew Hadamard difference families
ترجمه فارسی عنوان
سازه های مختلف خانواده هادامارد
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
In this paper, we generalize classical constructions of skew Hadamard difference families with two or four blocks in the additive groups of finite fields given by Szekeres (1969, 1971), Whiteman (1971) and Wallis-Whiteman (1972). In particular, we show that there exists a skew Hadamard difference family with 2uâ1 blocks in the additive group of the finite field of order qe for any prime power qâ¡2u+1(mod2u+1) with u⩾2 and any positive integer e. In the aforementioned papers of Szekeres, Whiteman, and Wallis-Whiteman, the constructions of skew Hadamard difference families with 2uâ1 (u=2 or 3) blocks in (Fqe,+) work only for restricted e;namely eâ¡1,2, or 3(mod4) when u=2, and eâ¡1(mod2) when u=3, respectively. Our more general construction, in particular, removes the restrictions on e. As a consequence, we obtain new infinite series of skew Hadamard difference families with two or four blocks, and hence skew Hadamard matrices.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 76, February 2019, Pages 73-81
Journal: European Journal of Combinatorics - Volume 76, February 2019, Pages 73-81
نویسندگان
Koji Momihara, Qing Xiang,