Various constructions for self-dual codes over rings and new binary self-dual codes

In this work, extension theorems are used for self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F^2m+uF^2m for m=1,2. The duality and distance preserving Gray maps from _F4+u_F4 to F₂+u_F2)² and F24 are used to obtain self-dual codes whose binary Gray images are [64,32,12]-extremal self-dual. An _F2+u_F2-extension is used and as binary images, 178 extremal binary self-dual codes of length 68 with new weight enumerators are obtained. Especially the first examples of codes with γ=3 and many codes with the rare γ=4,6 parameters are obtained. In addition to these, two hundred fifty doubly even self dual [96,48,16]-codes with new weight enumerators are obtained from four-circulant codes over _F4+u_F4. New extremal doubly even binary codes of lengths 80 and 88 are also found by the _F2+u_F2-lifts of binary four circulant codes and thus a lower bound on the number of non-isomorphic 3-(80, 16, 665) designs is modified.