Although IVDD is highly heritable, it is not a simple genetic disorder that can be tested for in the same way as Cord1 PRA or Lafora Disease which are also found in Dachshunds.
It is likely to be a disease caused by multiple genes as well as environmental and lifestyle factors. The genes involved almost certainly include those that code for chondroplasia (resulting in the Dachshund's short legs), but this cannot be the whole cause as non-chondrodystrophic breeds (with normal length legs) also suffer from IVDD.
Several genetic studies have been carried out and others are still underway, looking at the genetic basis of IVDD. In 2012 a team in Scandinavia identified an area of Chromosome 12 which was associated with genetic variations affecting disc calcification.
[The full paper is here]
The Breed Council has been working on a project with the AHT in the UK to look at the genetic basis of IVDD.