The present invention discloses a method for constructing a Golomb Costas sequence based on a high-order spread domain, which belongs to the field of
wireless communication technology. The method comprises the following steps: determining the order N of the Golomb Costas sequence to be constructed; and determining the order N of the Golomb Costas sequence to be constructed according to N=p. n ‑2, determine p, n, where p is a prime number and n is a positive integer, and explicitly state the
extended field GF (p n ); select an
irreducible polynomial of degree n with a leading coefficient of 1 on the prime field GF(p) as f(x), and clearly expand the field GF(p n ) in the form of elements, define the
extended field GF(p n ) two binary operations on elements in the GF(p n ) primitive elements and their powers, and
list the powers of primitive elements; in the
extended field GF(p n ) selects two primitive elements; calculates the placement coordinates and completes the construction of the Golomb Costas sequence. The present invention calculates the primitive elements of the extended domain and their powers by calling functions such as get_combins(p,n), modBKY(p,n,BY,BKY,res) and calc(p,n,BKY,res_product), and according to the construction formula of the Golomb Costas sequence and by searching the extended domain GF(p n )
list of powers of primitive elements, quickly calculate the placement coordinates of the Golomb Costas sequence, reduce the
workload of manual calculations, and improve the efficiency of constructing high-order Golomb Costas sequences based on extended domains. At the same time, it ensures the
correctness of the calculation of the placement coordinates of the Golomb Costas sequence, solving the difficult problem of constructing Golomb Costas sequences based on high-order extended domains.