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Cyclic Codes and Sequences From Generalized Coulter–Matthews Function

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2 Author(s)
Jinquan Luo ; Sch. of Math. Sci., Yangzhou Univ., Yangzhou ; Keqin Feng

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).

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IEEE Transactions on Information Theory  (Volume:54 ,  Issue: 12 )