کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5776843 1413643 2017 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Dimensions of three types of BCH codes over GF(q)
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Dimensions of three types of BCH codes over GF(q)
چکیده انگلیسی

BCH codes have been studied for over fifty years and widely employed in consumer devices, communication systems, and data storage systems. However, the dimension of BCH codes is settled only for a very small number of cases. In this paper, we study the dimensions of BCH codes over finite fields with three types of lengths n, namely n=qm−1, n=(qm−1)∕(q−1) and n=qm+1. For narrow-sense primitive BCH codes with designed distance δ, we investigate their dimensions for δ in the range 1≤δ≤q⌈m2⌉+1. For non-narrow sense primitive BCH codes, we provide two general formulas on their dimensions and give the dimensions explicitly in some cases. Furthermore, we settle the minimum distances of some primitive BCH codes. We also explore the dimensions of the BCH codes of lengths n=(qm−1)∕(q−1) and n=qm+1 over finite fields.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 340, Issue 8, August 2017, Pages 1910-1927
نویسندگان
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