If your connection is so bad that you are red barring the whole time, whether you benefit from it or not(Which I can see that you obviously don't, no offense, seriously), you will get a temporary ban, I would suggest tweaking your router settings, if you have changed your MTU for any reason, legitimate or not, change it back to default. Don't stream movies/youtube while playing Destiny or anything like that if your connection can't handle it. It's just temporary, Bungie rarely hands out permanent bans, mostly to console modders when you ruin the experience repeatedly after being banned in the past.
All bans are final, Bungie doesn't discuss bans/restrictions and all decisions are final. You're out of luck for the next week or so. I don't think you were intentionally doing anything wrong, but if you were having connection issues, they are pretty much cracking down on that kind of thing now.
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The bad thing is that bungie doesn't tell you why you are even restricted so I have no idea if it's because of my Internet connection however usually as soon as I feel any lag in my Internet I switch to my 4g lte network I don't enjoy bad connection they should notify the banned player the with the reason of the ban and how to fix it what bungie is doing is disrespectful
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There should be a warning issued! Along the lines of: "Attention, after repeated connection issues, this is too serve as a warning. Our systems have reported an ongoing connection issue, please check your router status or NAT to ensure optimal performance. If this remains an issue, you will be temporarily banned." This seems a little more........mature, than just outright bans with no warning or explanation. It may be there game but if theres no one left to play it then they have no game! Dedicated servers on there behalf would solve a lot of connection issues and would also prove they have faith in there game and fan base!