A (binary) formally self-dual code is a linear code whose weight enumerator is equal to that of its dual. Little is known about the existence of optimal subcodes of formally self-dual codes. In this paper we show that some optimal formally self-dual codes actually contain optimal subcodes by computing the optimum distance profiles (ODPs) of linear codes. We determine the ODPs of optimal formally self-dual codes with parameters \([16, 8, 5], [18, 9, 6], [20, 10, 6]\) and \([22,11,7]\) and show that they contain optimal subcodes with high minimum weights.
['Finley Freibert', 'Jon-Lark Kim']
Optimal subcodes of formally self-dual codes and their optimum distance profiles