We demonstrate distance-optimal few-weight binary linear codes using mixed alphabet ring methods, highlighting implications.
Key Points
The study identifies several families of distance-optimal binary linear codes using a mixed alphabet ring approach and simplicial complexes.
Most identified codes are self-orthogonal and minimal, demonstrating desirable characteristics in coding theory.
Analysis involves determining their Lee weight distributions and studying Gray images for efficient encoding strategies for applications in communication systems and data storage technologies. The results indicate the discovery of infinite families of three-weight projective codes and their connections to strongly l-walk-regular graphs.