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

In this paper, we give a matrix construction method for designing DNA codes that come from group rings. We show with our one can obtain reversible $$G^k$$ -codes of length kn, where $$k, n \in \mathbb {N},$$ over the finite commutative Frobenius ring R. employ to many $$\mathbb {F}_4$$ satisfy Hamming distance, reverse, reverse-complement and fixed GC-content constraints. Moreover, improve lowe...