Stripes forming in doped antiferromagnets between domains with opposite direction of staggered magnetization may be considered as domain walls in which filling with holes is enhanced in comparison with magnetic domains. It is not clear, what is the magnetic structure of these domain walls. Recent numerical results suggest that spin Peierls order may appear in doped antiferromagnets. In this work we analyze stability of stripes, or in other words domain walls, that have the shape of two leg ladders in which singlets form on rungs. A hole moving along a dimerized ladder is not confined. On the other hand, a tendency towards confinement may be observed in the motion of a hole in an antiferromagnet. A hopping hole shifts spins and creates linear defects in the magnetic structure on paths along which it has been moving. That confinement is not perfect because a hole may propagate in the antiferromagnetic spin background owing to some high order processes, the contribution of which to the total energy is small and is not decisive to stripe stability. Thus, we analyze motion of a hole along a stripe in terms of two components. The first component is motion of a hole in the domain wall. That component resembles propagation of a hole in the ladder with spin Peierls order on rungs. The second component represents motion of a hole after entering a domain. That motion is governed by the tendency towards confinement and formation of linear defects in the antiferromagnetic structure, so called strings. In order to analyze the stability of a bond-centered stripe we calculate its energy by means of the recurrence method which is suitable to analyze retractable motion of holes along strings. Later we make a comparison with the energy of a site-centered stripe. We deduce that the energy of a bond-centered stripe is lower than the energy of holes in the homogeneous antiferromagnetic background and lower than the energy of site-centered stripe for linear filling higher than 0.7.

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