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Authors
Sajjad, Muhammad
Bashir, Qamar
Haleemzai, Izatmand
Abdalrahem, Mushtaq K.
Hazzazi, Mohammad Mazyad
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Article History
Received: 22 September 2025
Accepted: 25 February 2026
First Online: 17 April 2026
Declarations
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: The authors declare no competing interests.
: We are extremely thankful to our great supervisor Professor Dr. Tariq Shah (late) who has guided us, taught us a lot, and supported us with all the invaluable guidance, enormous knowledge and undying support as we studied. He has made a significant contribution to our work in algebra, number theory, coding theory, and cryptography as well as to our personal and professional development, which is why his mentorship greatly benefited us. His wisdom, integrity and inspiration legacy still guides us. May his ghost receive peace at all times.
