Cyclic Codes and Sequences From Generalized Coulter–Matthews Function
Cyclic Codes and Sequences From Generalized Coulter–Matthews Function
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DOI：
10.1109/tit.2008.2006394
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发表时间：
2008-12
影响因子：
2.5
通讯作者：
Jinquan Luo;K. Feng
中科院分区：
文献类型：
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作者：
Jinquan Luo;K. Feng
在本文中，我们将研究与具有K/GCD的广义Coulter-Matthews函数X（PK+1）/2相关的指数总和SigmaxisInFQ X（Alphax（PK+1）/2+BETAX）。作为应用，我们获得以下内容：p-ary m序列的相关分布和pk+1/2度的M-序列的分布；二元具有两个零PI-1和PI的循环代码的重量分布 - （（PK+1）/2）。
In this paper, we will study the exponential sum SigmaxisinFq x(alphax(pk+1)/2+betax) that is related to the generalized Coulter-Matthews function x(pk+1)/2 with k/gcd. As applications, we obtain the following: the correlation distribution of a p-ary m-sequence and a decimated m-sequence of degree pk+1/2; the weight distribution of the cyclic code whose dual has two zeros pi-1 and pi-((pk+1)/2).