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Some new results on dimension and Bose distance for various classes of BCH codes
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2020-03-31 , DOI: 10.1016/j.ffa.2020.101673 Ahmed Cherchem , Abdelillah Jamous , Hongwei Liu , Youcef Maouche
中文翻译:
各种BCH码的尺寸和Bose距离的一些新结果
更新日期:2020-03-31
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2020-03-31 , DOI: 10.1016/j.ffa.2020.101673 Ahmed Cherchem , Abdelillah Jamous , Hongwei Liu , Youcef Maouche
In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over with designed distance for all , where q is a prime power and is a positive integer. As a consequence, we obtain an affirmative answer to two conjectures proposed by C. Ding in 2015. Furthermore, using the previous part, we extend some results of Yue and Hu [16], and we give the dimension and, in some cases, the Bose distance for a large designed distance in the range for , where if m is odd, and if m is even.
中文翻译:
各种BCH码的尺寸和Bose距离的一些新结果
在本文中,我们给出了窄感知原始BCH码的两个子类的维数和最小距离 设计距离 对所有人 ,其中q是素数是一个正整数。结果,我们获得了丁丁在2015年提出的两个猜想的肯定答案。此外,在前一部分的基础上,我们扩展了岳和胡的某些结果[16],并给出了维数,在某些情况下,在范围内较大的设计距离下的玻色距离 对于 ,在哪里 如果m是奇数,并且如果m是偶数