I am in camp with people who say that say that the effect on corn planted into rye is that the rye ties up nutrients, not alleopathy from rye. I have posted the following pictures before. They show the corn plants that were planted no-till in soil with no residue and in soil that had rye growing. The corn was planted 6/9-10/ 2015. Both fields have continous no-till 20+ years. No starter or other fertilizer was applied. As you can tell from the pictures the corn in the rye cover doesn't have a nice green color to it compared to the corn in the bare soil. The rye was sprayed two days after the corn was planted. 

(harlans sq nef corn planted 6 12 2015.jpg)

(harlans sq nef corn 4 collar nmc 7 07 2015.jpg)

(home place sm n o s 5 collar 7 5 2015.jpg)

harlans sq nef corn planted 6 12 2015.jpg (312KB - 195 downloads)

harlans sq nef corn 4 collar nmc 7 07 2015.jpg (258KB - 198 downloads)

home place sm n o s 5 collar 7 5 2015.jpg (305KB - 193 downloads)