Extremal binary self-dual codes

Abstract

In this correspondence, we investigate binary extremal self-dual codes. Numerous extremal self-dual codes and interesting self-dual codes with minimum weight d=14 and 16 are constructed. In particular, the first extremal Type I [86,43,16] code and new extremal self-dual codes with weight enumerators which were not previously known to exist for lengths 40,50,52 and 54 are constructed. We also determine the possible weight enumerators for extremal Type I codes of lengths 66-100.