On Automorphism Group of Cyclic Codes with Given Length

Cyclic codes are a significant subclass of linear block codes, known for their efficiency and the ability to support fast coding algorithms. These codes play a crucial role in various fields, including communication systems, information security, and data storage. This paper mainly studies binary cyclic codes of lengths <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p q$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 p^{n}$</tex> over <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{F}_{2}$</tex> for a positive integer <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> are different odd prime numbers. Using a matrix representation technique for cyclic codewords, the automorphism groups of cyclic codes with these given lengths are classified.