On Some Quaternary Self-Orthogonal Codes

Abstract

This paper studies families of self-orthogonal codes over \(\mathbb{Z}_4\). We show that the simplex codes (of Type \(a\) and Type \(\beta\)) are self-orthogonal. We answer the question of \(\mathbb{Z}_4\)-linearity for some codes obtained from projective planes of even order. A new family of self-orthogonal codes over \(\mathbb{Z}_4\) is constructed via projective planes of odd order. Properties such as self-orthogonality, weight distribution, etc. are studied. Finally, some self-orthogonal codes constructed from twistulant matrices are presented.