商环Z[i]/《pn(1+i)》中的乘法单位群

一些复整数构成的有限乘法群可被用来获得正交调幅信号空间以及设计纠错码.假设p是一个奇素数,n是一个正整数.证明了复整数环Z√-1]模理想的乘法单位群的一个子群可被用来获得正交调幅信号空间.这样的空间具有4p2n-2点并具有对称性等很好的几何性质.子群也可被用来设计改正一些错误的纠错码.

The multiplicative group of units in the quotient ring Z[i]/《Pn(1+i)》

It was shown that some finite multiplicative groups of complex integers can be used to obtain quadrature amplitude modulation (QAM) signal spaces and to design errorcorrecting codes. This paper shows that one subgroup of the multiplicative group of units in the complex integer ring Z√-1], modulo ideal 〈pn(1+i)〉, can be used to obtain a QAM signal space of 4p2n-2 points with good geometrical properties, where p is an odd prime. These QAM signals can be coded such that a differentially coherent method can be applied to demodulate the QAM signals.