According to the official document:
Your app can be hosted on Traditional ASP.NET or ASP.NET Core (With Full .NET Framework). ASP.NET Core with .NET Core support will be added in near future. You can track that by following this issue.
It seems that this feature will be added later.
Clearly can we develop app with bit-framework in Linux based OS by using of .Net Core and Visual Studio Code C# extension?
1- There are a few types which are going to be introduced in .NET Core 2.1 and we rely on them in bit framework based apps.
2- Our background job worker is not migrated yet. (Based on micro service/modular based architecture of bit framework, you don't have to install/use that, so you can ignore this for now)
3- Our typescript-javascript code generator is based on Roslyn and Roslyn itself is cross-platform. We're going to release msbuild version of our code generator, so you can use it on top of any IDE such as Rider etc.
In case you've access to Visual Studio and Windows, start developing based on our ASP.NET core / full .net framework version, and there will be no code change for you when you switch to .NET Core. Remember to use Bit.Data.EntityFrameworkCore instead of Bit.Data.EntityFramework, as Bit.Data.EntityFramework will not be migrated to .NET Core. (EF itself will not be migrated based on decisions of data team of Microsoft)