广义平方素数码

General Quadratic Prime Codes

基于有限扩域与有限基域的对应关系,该文将素数码的构造思想延伸到有限扩域,基于有限扩域乘法,以一般二次既约多项式为模,构造出一类周期增大、序列数目增多的跳频序列族——广义平方素数码,该码具有理想汉明自相关特性和最大互相关值为2的几乎理想的汉明互相关特性。通过分组,得到具有最大互相关值为1的理想汉明互相关特性的跳频序列组。

Based on the relationship between the extension Galois fields and the prime Galois fields, this paper presents a new construction of frequency-hopping sequences, here designated as general quadratic prime codes, by expanding the construct idea of prime codes to extension Galois fields. Taking a general quadratic irreducible polynomial as the module and based on the multiplication of extension Galois fields, quadratic prime codes with more sequences and longer period possess ideal Hamming autocorrelation and nearly ideal Hamming cross-correlation properties of no greater than two. Furthermore, general quadratic prime codes can be further partitioned to get frequency hopping sequences groups in which the maximum Hamming cross-correlation between any two FH sequences in the same group is at most one.