کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895578 | 1630349 | 2018 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A family of optimal ternary cyclic codes from the Niho-type exponent
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. The objective of this paper is to present a family of optimal ternary cyclic codes from the Niho-type exponent. Specifically, for an odd integer m and a positive integer r with 4râ¡1(modm), a family of cyclic codes C(u,v) of length 3mâ1 over GF(3) with two nonzeros βu and βv is studied, where β is a generator of GF(3m)â, u=(3m+1)/2 and v=3r+2 is the ternary Niho-type exponent. The parameters of this family of cyclic codes are determined. It turns out that C(u,v) is optimal with respect to the Sphere Packing bound if 9â¤m and otherwise almost optimal. Thanks to a recent proof of the Dobbertin-Helleseth-Kumar-Martin conjecture by Katz and Langevin, the dual of this family of cyclic codes is shown to have at most five nonzero weights.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 54, November 2018, Pages 101-112
Journal: Finite Fields and Their Applications - Volume 54, November 2018, Pages 101-112
نویسندگان
Haode Yan, Zhengchun Zhou, Xiaoni Du,