Self-dual [24, 12, 8] quaternary codes with a nontrivial automorphism of order 3
The Hermitian inner product of \(u= (u_1,u_2,\dots, u_n)\), \(v= (v_1,v_2,\dots, v_n)\in \text{GF}(4)^n\) is given by \((u,v)= \sum^n_{i=1} u_i v^2_i\). The minimum weight \(d\) of a self-dual \([n,n/2,d]\) quaternary code satisfies the bound \(d\leq 2\lfloor n/6\rfloor+ 2\). The code is called extremal if this bound is met with equality. It is known that a \([24,12,10]\) extremal self-dual code over \(\text{GF}(4)\) does not exist. The author obtains up to equivalence all (Hermitian) self-dual \([24,12,8]\) codes over \(\text{GF}(4)\) which have a non-trivial automorphism of order 3. There are exactly 205 inequivalent such codes. These codes are optimal, self-dual and have the highest possible minimum distance for this length.
scientific article; zbMATH DE number 1763660
scientific article