Catalysis of the cleavage of glycosidic bonds through a beta-elimination reaction on alginate, a linear polysaccharide consisting of guluronate (G) and mannuronate (M) as the monomer constituents. An oligoalginate is a linear polymer of two, three or four units of (1->4)-alpha-L-guluronic acid and beta-D-mannuronic acid, releasing monosaccharides with 4-deoxy-alpha-L-erythro-hex-4-enopyranuronosyl groups at their ends.