Extension theorems for self-dual codes over rings and new binary self-dual codes

Abstract

In this work, extension theorems are generalized to self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F_2^m+uF_2^m for m = 1, 2. The duality and distance preserving Gray maps from F4 +uF4 to (F_2 +uF_2)^2 and (F_4)^2 are used to obtain self-dual codes whose binary Gray images are [64,32,12]-extremal self-dual. An F_2+uF_2-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 gamma=3 and many codes with the rare gamma= 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 F_4 + uF_4. New extremal doubly even binary codes of lengths 80 and 88 are also found by the F_2+uF_2-lifts of binary four circulant codes and a corresponding result about 3-designs is stated.