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This is a first step toward the determination of the parameters of two-point codes on a Hermitian curve. We describe the dimension of such codes and determine the minimum distance of some two-point codes.

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This is the second part of the series of papers devoted to the determination of the minimum distance of two-point codes on a Hermitian curve. We study the case where the minimum distance agrees with the designed one. In order to construct a function which gives a codeword with the designed minimum distance, we use functions arising from conics in the projective plane.

This is a continuation of the previous papers [3,4,5]. We finish determining the minimum distance of two-point codes on a Hermitian curve.