In [Hastings et al 2014] it is stated that the code distance of a logical qubit stored using dislocations is 2L + O(1), where L is the separation between the dislocation twists. This code distance assumed only physical X and Z errors are permitted. This short note shows that, when Y errors are allowed, the code distance reduces to L + O(1). See Figure 1.
Cite
@article{arxiv.1910.00363,
title = {Surface code dislocations have code distance L+O(1)},
author = {Craig Gidney},
journal= {arXiv preprint arXiv:1910.00363},
year = {2019}
}