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An implementation of estimating the two-to-two $K$-matrix from finite-volumeenergies based on the L\"uscher formalism and involving a Hermitian matrixknown as the "box matrix" is described. The method includes higher partialwaves and multiple decay channels. Two fitting procedures for estimating the$K$-matrix parameters, which properly incorporate all statistical covariances,are discussed. Formulas and software for handling total spins up to $S=2$ andorbital angular momenta up to $L=6$ are obtained for total momenta in severaldirections. First tests involving $\rho$-meson decay to two pions include the$L=3$ and $L=5$ partial waves, and the contributions from these higher wavesare found to be negligible in the elastic energy range.

Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies