On the performance of optimal double circulant even codes

In this note, we investigate the performance of optimal double circulant even codes which are not self-dual, as measured by the decoding error probability in bounded distance decoding. To do this, we classify the optimal double circulant even codes that are not self-dual which have the smallest weight distribution for lengths up to 72. We also give some restrictions on the weight enumerators of (extremal) selfdual [54, 27, 10] codes with shadows of minimum weight 3. Finally, we consider the performance of extremal self-dual codes of lengths 88 and 112.