کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895584 | 1630349 | 2018 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Minimal linear codes over finite fields
ترجمه فارسی عنوان
کدهای خطی حداقل در زمینه های
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research topic in coding theory and cryptography. Ashikhmin and Barg showed that wmin/wmax>(qâ1)/q is a sufficient condition for a linear code over the finite field GF(q) to be minimal, where q is a prime power, wmin and wmax denote the minimum and maximum nonzero weights in the code, respectively. The first objective of this paper is to present a sufficient and necessary condition for linear codes over finite fields to be minimal. The second objective of this paper is to construct an infinite family of ternary minimal linear codes satisfying wmin/wmaxâ¤2/3. To the best of our knowledge, this is the first infinite family of nonbinary minimal linear codes violating Ashikhmin and Barg's condition.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 54, November 2018, Pages 176-196
Journal: Finite Fields and Their Applications - Volume 54, November 2018, Pages 176-196
نویسندگان
Ziling Heng, Cunsheng Ding, Zhengchun Zhou,