单圈T-函数的2-adic复杂度和1-错2-adic复杂度

The 2-adic complexity and the 1-error 2-adic complexity of single cycle T-functions

研究了由2nF上单圈T-函数所导出权位序列的2-adic复杂度,设j为整数,0≤j≤n?1。结论表明,第j权位序列2-adic复杂度的上界为2lb(2 1)j?。另外,讨论了与所有单圈T-函数所导出第j权位序列相对应的2-adic整数的分布,分布情况说明这个上界是可以达到的。最后,研究了权位序列的1-错2-adic复杂度。研究结果表明对所有1≤j≤n?1,权位序列jx的1-错2-adic复杂度都与其2-adic复杂度相同。

The 2-adic complexities of the coordinate sequences derived from single cycle T-functions over 2nF were in-vestigated. Let j be an integer such that 0 1≤ j≤n-1. It is shown that the 2-adic complexity of the j th coordinate sequence is upper bounded by lb（2^2′＋1）. The distribution of the corresponding 2-adic number associated with the j th coordinate sequence of all single cycle T-functions was also discussed, which implies that the upper bound is attainable. Moreover, 1-error 2-adic complexity was also studied. It was proved that the 1-error 2-adic complexity of the j th coor-dinate sequence is equal to its 2-adic complexity except for j=0 .