A NEW APPLICATION TO CODING THEORY VIA GUGLIELMO NUMBERS

This paper describes a new coding and decoding technique based on the Guglielmo sequence. Our version isbased on a blocked message matrix, with every message matrix encrypted using a special key. The amount of information transmitted over the internet has increased as internetuse has become more prevalent. Consequently, the importance of the algorithms used in data encryption methodshas increased. The proposed method is fast because it isbased on fundamental matrix operations and is suitable forcryptographic applications due to its use of the ASCII character encoding system. For this reason, it differs from classical algebraic methods described in the literature. Using447Received: July 30, 2025International Journal of Applied Mathematics Volume 38 No. 4s, 2025 ISSN: 1311-1728 (printed version); ISSN: 1314-8060 (on-line version) Guglielmo numbers we define Guglielmo G-matrices. Wecan process any given message with a special encryptionand we can decode the encrypted massage with the methodwe use.Math. Subject Classification: 68P30, 11B39, 11B50,11B37, 11T71, 11B83