Linear codes from arcs and quadrics

The article delves into the construction of linear codes from geometric objects such as KM-arcs, hyperovals, and elliptic quadrics, using a novel polar coordinate representation. It explores the applications of these codes in cryptography and quantum error correction, highlighting the construction of LCD codes with few weights and self-orthogonal codes leading to quantum codes. The paper also emphasizes the potential of these methods in constructing quantum error-correcting codes with optimal parameters. The research is conducted over large finite fields of characteristic 2, offering new and improved codes compared to existing literature.