Construction for both self-dual codes and LCD codes

Abstract

From a given $[n,k]$ code $C$, we give a method for constructing many $[n,k]$ codes $C^{\prime }$ such that the hull dimensions of $C$ and $C^{\prime }$ are identical. This method can be applied to constructions of both self-dual codes and linear complementary dual codes (LCD codes for short). Using the method, we construct 661 new inequivalent extremal doubly even $[56,28,12]$ codes. Furthermore, constructing LCD codes by the method, we improve some of the previously known lower bounds on the largest minimum weights of binary LCD codes of length $n=26,28\le n\le 40$.

References in corpus (1)

• Construction of binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes