New extremal binary self-dual codes of length 58 as R3-lifts from the shortened binary [formula omitted] Hamming code

Abstract

In this correspondence, a lift of the shortened binary [8,4,4] Hamming code to the ring R3 is described. Using this lift, a family of self-dual codes over R3 of length 7 are obtained. By taking the binary images of these codes and applying the extension method given in [15], 11 new extremal binary self-dual [58,29,10] codes with new weight enumerators are found which were not previously known to exist.