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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

In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over Fq with designed distance δ=aqm11(resp. δ=aqm1q1) for all 1aq1, where q is a prime power and m>1 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 [aqm1q1,aqm1q1+T] for 0aq2, where T=qm+121 if m is odd, and T=2qm21 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 Fq 设计距离 δ=一种q-1个-1个分别 δ=一种q-1个q-1个 对所有人 1个一种q-1个,其中q是素数>1个是一个正整数。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[一种q-1个q-1个一种q-1个q-1个+Ť] 对于 0一种q-2,在哪里 Ť=q+1个2-1个如果m是奇数,并且Ť=2q2-1个如果m是偶数

更新日期:2020-03-31
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