On the non Z/sub 4/-linearity of certain good binary codes
J. Fields, Philippe Gaborit · IEEE Transactions on Information Theory · 1999
In this correspondence we prove that any extremal doubly-even self-dual linear binary code of length 48 is not Z/sub 4/-linear. We also show that the putative extremal doubly-even self-dual linear binary codes of lengths 72 and 96 with minimum weight, respectively, 16 and 20, cannot be constructed as the Gray images of linear codes over Z/sub 4/.