For example, Linux MD RAID 5 uses XOR, and RAID 6 uses Galois fields. [1][2]
0: https://www.itprotoday.com/storage/erasure-coding-vs-raid-which-right-and-when
1: https://raid.wiki.kernel.org/index.php/A_guide_to_mdadm#Raid_5
2: http://igoro.com/archive/how-raid-6-dual-parity-calculation-works/