کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4583220 | 1333889 | 2007 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
3-Designs from all Z4-Goethals-like codes with block size 7 and 8
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We construct a family of simple 3-(m2,8,14(m2−8)/3) designs, with odd m⩾5, from all Z4-Goethals-like codes Gk. In addition, these designs imply the existence of other design families with the same parameters as the designs constructed from the Z4-Goethals code G1, i.e. the designs with a block size 7 by Shin, Kumar, and Helleseth and the designs with a block size 8 by Ranto. In the existence proofs we count the number of solutions to certain systems of equations over finite fields and use properties of Dickson and linearized polynomials. Also, the nonequivalence of the designs from different Goethals-like codes is considered.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 13, Issue 4, November 2007, Pages 815-827
Journal: Finite Fields and Their Applications - Volume 13, Issue 4, November 2007, Pages 815-827