A new scheme for building good self-dual block codes

We present a very simple multi-stage encoding scheme of self-dual codes using a [8,4,4] extended Hamming code as short base code and bit permutations (or interleavers as in turbo-codes) between stages. We describe several examples of interleavers in order to build some extremal codes, with a minimum number of stages, such as the [24,12,8] Golay code, [32,16,8], [64,32,12], and [88,44,16] codes. For length 32, we show how to build the 5 non-equivalent extremal QR, RM, F, G, U [32,16,8] self-dual codes. We conjecture that this encoding scheme may find good rate-1/2 long block codes.