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From a given $[n, k]$ code $C$, we give a method for constructing many $[n,k]$ codes $C'$ such that the hull dimensions of $C$ and $C'$ are identical.This method can be applied to constructions of both self-dual codes and linearcomplementary dual codes (LCD codes for short). Using the method, we construct661 new inequivalent extremal doubly even $[56, 28, 12]$ codes. Furthermore,constructing LCD codes by the method, we improve some of the previously knownlower bounds on the largest minimum weights of binary LCD codes of length$n=26,28 \le n \le 40$.

Construction for both self-dual codes and LCD codes