On Infinite Families of Narrow-Sense Antiprimitive BCH Codes Admitting 3-Transitive Automorphism Groups and Their Consequences

The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic that have found numerous applications in error correction and notably quantum information processing. They widely used data storage communication systems. A attractive BCH is the narrow-sense over Galois field ${\mathrm {GF}}(q)$ with length notation="LaTeX">$q+1$ , which closely related to action projective general linear group degree two on line. Despite its interest, not much known about this class codes. This paper aims study some within specifically antiprimitive (these also complementary duals (LCD) interesting practical recent cryptography, among other benefits). We shall use tools combine arguments from algebraic coding theory, combinatorial designs, theory (group actions, representation finite groups, etc.) investigate Codes extend results literature. Notably, dimension, minimum distance notation="LaTeX">$q$ -ary their determined paper. dual derived include almost MDS Furthermore, classification {PGL}}(2, p^{m})$ -invariant {GF}}(p^{h})$ completed. As an application result, notation="LaTeX">$p$ -ranks all incidence structures invariant under determined. infinite families admitting 3-transitive automorphism obtained. Via these codes, coding-theory approach constructing Witt spherical geometry designs presented. proposed good candidates for permutation decoding, as they relatively large automorphisms.