Self-orthogonal designs and codes from the symplectic groups S4(3)S4(3) and S4(4)S4(4)

We determine self-orthogonal designs and self-orthogonal codes from the primitive representations of the projective symplectic groups S4(3)S4(3) and S4(4)S4(4), respectively. We establish some properties of these codes and the nature of some classes of codewords. Some of the codes are optimal or near optimal for the given length and dimension. The dual codes of some designs and those of some complementary designs admit majority logic decoding.