A cellulose reactive glyoxalated copolymer composition and methods of producing and using the glyoxalated copolymer composition to, for instance, strengthen paper or board are discussed. A glyoxalated copolymer composition includes an aqueous medium containing a glyoxalated copolymer, wherein the glyoxalated copolymer is obtained by reaction in an aqueous reaction medium of a dry weight ratio of glyoxalxationic copolymer. The cationic copolymer can have a weight average molecular weight of about 120,000 to about 1 million Daltons, the cationic copolymer can include diallyldimethylammonium halide monomer and acrylamide monomer, and a ratio a ratio of the weight average molecular weight of the cationic copolymer before glyoxalation to weight % of diallyldimethylammonium halide monomer making up the cationic copolymer before glyoxalation can be equal to or greater than 4,000 or range from 4,000 to 40,000 Daltons/weight %.