  The Majorana code is an example of a stabilizer code where the quantum
information is stored in a system supporting well-separated Majorana Bound
States (MBSs). We focus on one-dimensional realizations of the Majorana code,
as well as networks of such structures, and investigate their lifetime when
coupled to a parity-preserving thermal environment. We apply the Davies
prescription, a standard method that describes the basic aspects of a thermal
environment, and derive a master equation in the Born-Markov limit. We first
focus on a single wire with immobile MBSs and perform error correction to
annihilate thermal excitations. In the high-temperature limit, we show both
analytically and numerically that the lifetime of the Majorana qubit grows
logarithmically with the size of the wire. We then study a trijunction with
four MBSs when braiding is executed. We study the occurrence of dangerous error
processes that prevent the lifetime of the Majorana code from growing with the
size of the trijunction. The origin of the dangerous processes is the braiding
itself, which separates pairs of excitations and renders the noise nonlocal;
these processes arise from the basic constraints of moving MBSs in 1D
structures. We confirm our predictions with Monte Carlo simulations in the
low-temperature regime, i.e. the regime of practical relevance. Our results put
a restriction on the degree of self-correction of this particular 1D
topological quantum computing architecture.
