It actually does have galvanized in the description, so that material is just what you want. It's the first bullet on the right under the price. Galvanization has nothing to do with strength, the 19 gage is what gives you strength - 19 gage refers to the diameter of the wire - the larger diameter the stronger the wire. But the naming system is weird, so 23 gage has a smaller diameter than 19 gage. You can look up "wire gage" on google and learn more about how they grade/classify wire. Galvanization means that it has been dipped in a vat of molten zinc as part of the hardware cloth manufacturing process. A layer of zinc stays on the steel once it cools. This layer of zinc is more reactive with moisture than the steel, so it oxidizes when it is around moisture instead of letting the steel rust. The zinc functions as a sacrificial anode to protect the steel. The white coating that you see on the hardware cloth over time is the zinc oxidizing. Once all the zinc is oxidized, the steel will start to rust, but this usually takes about 15-20 years depending on the weather where you're using the hardware cloth and how much moisture it sees. If the hardware cloth sees ground contact, I'd check it every couple years to be sure it hasn't degraded yet.
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100 ft of galvanized hardware cloth is difficult to find in store - I buy mine off of Amazon, although you could probably also order through the hardware store online for 100ft lengths. Also try feedstores - they carry fencing and may have some.