New lower bounds for the Shannon capacity of odd cycles

The Shannon capacity of a graph G is defined as (Formula presented.) where (Formula presented.) is the independence number of G. The Shannon capacity of the cycle (Formula presented.) on 5 vertices was determined by Lovász in 1979, but the Shannon capacity of a cycle (Formula presented.) for general odd p remains one of the most notorious open problems in information theory. By prescribing stabilizers for the independent sets in (Formula presented.) and using stochastic search methods, we show that (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.). This leads to improved lower bounds on the Shannon capacity of (Formula presented.) and (Formula presented.): (Formula presented.) and (Formula presented.).