差集偶与几乎差集偶的新构造

New Constructions of Difference Set Pairs and Almost Difference Set Pairs

摘要: 具有良好自相关性质的信号序列在众多领域中有广泛的应用。良好的自相关性质可以转化为集合作差后元素出现次数的问题，对此有独特要求的差集偶和几乎差集偶是构造良好的自相关性质信号序列的重要方法。本文使用有限域Z_p中八阶分圆类构造出参数为的(8f+1,2f,2f,0,f/2)差集偶与参数为(8f+1,2f,2f,0,f/2,(f+2)/2)的几乎差集偶，其中奇素数p=8f+1=a²+2b²=(2-a)²+4b²，f是偶数。

Abstract: Signal sequences with good autocorrelation properties are widely used in many fields. Good autocorrelation property can be transformed into the problem of the number of elements after subtraction of two sets. Difference set pairs and almost difference set pairs with the precisely requirements are important methods to construct good autocorrelation signal sequences. Difference set pairs with parameter (8f+1,2f,2f,0,f/2) and almost difference set pairs with parameter (8f+1,2f,2f,0,f/2,(f+2)/2) are constructed by using cyclotomic classes of order eight in finite field Z_p, where p=8f+1=a²+2b²=(2-a)²+4b², and f is an even number.