LCD codes over finite fields
Nouara Zoubir, Kenza Guenda, Padmapani Seneviratne, Thomas Aaron Gulliver · Discrete Mathematics Algorithms and Applications · 2024
In this paper, we introduce several new construction techniques of linear complimentary dual (LCD) codes. First, we show that if a LCD code is fixed by a transitive automorphism group, then the punctured code is also LCD. We show that several important families such as anti-primitive BCH codes and extended Gabidulin codes are LCD. Finally relationships among self-dual codes, [Formula: see text]-orthogonal matrices and LCD codes are studied. As an application we give LCD codes from Paley-type bipartite graph and from punctured MacDonalds codes. Further, we give a bound on some LCD codes.