On automorphism groups of binary cyclic codes

Cyclic codes, as a significant subclass of linear codes, can be constructed and analyzed using algebraic methods. Due to its cyclic nature, they have efficient encoding and decoding algorithms. To date, cyclic codes have found applications in various domains, including consumer electronics, data storage systems, and communication systems. In this paper, we investigate the full automorphism groups of binary cyclic codes. A matrix presentation technique of cyclic codewords is introduced, which subsequently serves well for presenting binary cyclic codes of long lengths. These constructions are significantly useful in facilitating the determination of the full automorphism groups of binary cyclic codes of specified lengths.