An Incremental Computational Strategy for Constructing Explicit W(44,k) for All Odd Weights

This repository contains the computational materials associated with the preprint "An Incremental Computational Strategy for Constructing Explicit W(44,k) for All Odd Weights" by Adrián Macías-Quintero. The work presents a computational construction of weighing matrices of order 44 for every odd weight k = 1, 3, 5, ..., 43. The construction is based on a Goethals-Seidel array of four circulant blocks of order 11. Rather than searching directly over the 44 x 44 matrix entries, the algorithm searches over four ternary generating sequences A, B, C, D in {-1, 0, 1}^11. A simulated-annealing procedure is used within this discrete search space, organized as an incremental chain in which a solution for weight k-2 is used as the seed for the search at weight k. The deposited materials include the preprint in PDF and LaTeX format, the principal Python solver, and machine-readable representations of the generated solutions. The computational record contains explicit solutions for all 22 odd weights from 1 to 43, together with the corresponding generating sequences and 44 x 44 matrices. Each reported matrix is reconstructed and checked using exact integer arithmetic. The verification checks the matrix dimensions, entries in {-1, 0, 1}, the prescribed row and column weights, and the identities W W^T = k I_44 and W^T W = k I_44. In the recorded computation, the complete incremental chain from W(44,1) to W(44,43) was completed in a total wall-clock time of 4 minutes and 38 seconds. This repository provides a reproducible and citable computational record of the constructions, including the source code, generated solution data, and computational documentation.