Code Recovery using algebraic-geometric approaches becomes computationally expensive with the cardinality of the field and complex code structures. In response, we propose a low-complexity algorithm that utilizes structures in algebraic-geometric codes over finite fields. The low-complexity algorithm to locally recover algebraic codes over finite fields (i.e., 𝑙𝑟𝑐 algorithm) is defined based on a sparse matrix factorization that computes the inverse of an (r+1) x r generator matrix, whose elements are defined by the points on the surface in P³ over the finite field 𝔽q with locality r. We have shown that the (𝑙𝑟𝑐 algorithm) reduces the complexity from O(n³) to O(nlogn) for the n = 2ˢ (s ≥ 1)> r length codeword. The extended 𝑙𝑟𝑐 algorithm is proposed to globally recover codes over finite fields. As a benchmark, we design structured neural networks (StNNs), i.e., DFT-StNN and DCT-StNN, based on the factorization of the generator matrix to globally recover codes. Numerical Simulations were conducted to compare the performance of the extended 𝑙𝑟𝑐 algorithm in global recovery codes, with brute-force calculation, DFT-StNN, DCT-StNN, and a feedforward neural network for codewords with lengths from n=6, 12, 27, 48, 96, and 210, having locality 2 for points on the surface P³ over the finite field 𝔽q. Our empirical results demonstrate that the extended 𝑙𝑟𝑐 algorithm achieves the lowest flops, the highest accuracy with an error order 10⁻¹⁶ for all length codewords, compared to brute-force calculations, DFT-StNN, DCT-StNN, and the feedforward neural network.