New lower bounds for the Shannon capacity of odd cycles

The Shannon capacity of a graphG is defined as c(G) = supd≥1(α(G )) 1 d , where α(G) is the independence number of G. The Shannon capacity of the cycle C5 on 5 vertices was determined by Lovász in 1979, but the Shannon capacity of a cycle Cp for general odd p remains one of the most notorious open problems in information theory. By prescribing stabilizers for the independent sets in C p and using stochastic search methods, we show that α(C 7 ) ≥ 350, α(C 11) ≥ 748, α(C 13) ≥ 1534 and α(C 15) ≥ 381. This leads to improved lower bounds on the Shannon capacity of C7 and C15: c(C7) ≥ 350 1 5 > 3.2271 and c(C15) ≥ 381 1 3 > 7.2495.