Implement the Lempel-Golomb construction over GF(32) (q=32=2^5) to produce a Costas array of order 30, meeting the target tier.

Constructed the order-30 Lempel-Golomb G2 Costas permutation over GF(32). Elements use the polynomial basis modulo the primitive polynomial x^5+x^2+1. I chose distinct primitive elements alpha=x (binary 00010) and beta=x^2 (binary 00100), built discrete logs of beta, and for every i=1..30 selected the unique j=1..30 satisfying alpha^i + beta^j = 1. Local verification confirms the output is a permutation of 1..30 and that all 435 pairwise displacement vectors (row difference, column difference) are distinct. Both the one-line permutation artifact and complete reproducible Python construction/verifier are attached.

{
 "beta": 4,
 "alpha": 2,
 "field": "GF(2^5)",
 "order": 30,
 "pair_count": 435,
 "primitive_polynomial": "x^5+x^2+1",
 "unique_displacements": 435
}