COSTAS阵列的一些代数属性

Algebraic Properties of COSTAS Arrays

COSTAS阵列在信号处理等领域有广泛的应用,将COSTAS阵列为核心技术的McEliece系统引入NC的身份鉴别等安全协议,将大大提高NC的安全性。文章探讨了COSTAS阵列的代数属性,找出生成COSTAS阵列的标准型置换多项式,定出q=3,4,5,7的所有的置换多项式及COSTAS阵列所属于的置换多项式类,并发现Golomb构造法或Welch构造法可以通过非循环移位生成许多COSTAS阵列及相应的等价COSTAS阵列。

COSTAS arrays have profound appliances in manyfields including the signal process.If we can produce the McEliece public key system to apply to the security protocol in the NC(network computer)by using the kernel technology of COSTAS arrays,the security of NC will be enhanced.In this paper,we discuss the algebra properties of Costas arrays,ex-pose that permutation polynomials can produce the COSTAS ar-rays through classifying all the permutation polynomials in the finite fields.Moreover,we discover all the permutation polyno-mials and the COSTAS arrays belong to the corresponding classes of the polynomials in the finite fields Fq when q=3,4,5and find out COSTAS arrays and the equivalence COSTAS ar-rays which is either from construction of Golomb's or Welch's can produce many COSTAS arrays by non-periodic shift when q=3,4,5,7.Finally,we present the future research approach.