Rm的置换多项式与COSTAS矩阵

PERMUTATION POLYNOMIALS OVER THE RESIDUE CLASSS RING (Z/(M) ) AND COSTAS ARRAYS

本文给出了多项式ｈｋ（Ｘ）＝１十ｘ十ｘ２＋…＋ｘｋ置换剩余类环Ｒｍ（Ｚ／（ｍ））的充分必要条件；证明了Ｒｍ的纯奇次置换多项式ｆ（ｘ）不能生成ｍ×ｍ（ｍ≥４）的Ｃｏｓｔａｓ矩阵．并深人讨论了迪克逊多项式ｇｋ（ｘ，ａ）和ｈｋ（ｘ）与Ｃｏｓｔａｓ矩阵的关系．

The sufficient and neccessary condition for hk (x)= 1 + x + x2+…+xk to permute residue class ring Z/(m) to given, and the permutation polynomials which only contain odd degree items over Z/(m) (m34) can't produce the m × m Costas arrays, and the relations between Dickson polynomials gk (x,a ) and Costas arrays are thoroughly discussed in the paper.