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The evolution of the crystal structure and the magnetic properties was investigated in the La0.5Sr0.5CoO(3-δ) (0 < δ < 0.3) system as a function of the oxygen deficit δ. Compounds with a low oxygen deficit (δ < 0.1) are shown to be predominantly ferromagnetic, while further increase (δ > 0.1) gradually changes the magnetic structure from ferromagnetic to G-type antiferromagnetic and causes a structural transition from rhombohedral to cubic symmetry. Resistivity and magnetoresistance at low temperature increase with increasing of oxygen vacancies. It is argued that oxygen reduction facilitates stabilization of the high spin state of Co(3+) ions. Antiferromagnetic interactions between cobalt ions in the high spin state are found to dominate in compounds with the oxygen deficit δ > 0.18.