Head of the Research Group

Professor Adel N. Alahmadi

Deanship of Scientific Research
King Abdulaziz University, Jeddah, Saudi Arabia
Email: dsr-asa@kau.edu.sa

Brief History

The Research Group of Algebraic Structures and its Applications is a youthful but vigorous group which was established in September 2017. Its foundation was due to the dedicated efforts of various members who had a solid background in algebra and a common interest in its applications. The aim of their activities firstly was to attract local professors and graduate students by organizing series of lectures presented by famous scientists in algebra and its applications. Back in 2010 an important three-week crash course on algebraic coding theory was given by the Parisian Professor Patrick Solé. Other crash courses were organized later as continuations of series of these varied courses in their related subjects and applications with algebra. This area of coding theory applies algebraic structures such as finite fields and rings to error-correcting communication protocols that are strongly sought after by engineers for many applications such as data transfer in noisy environments, or calculations in quantum computers. Following these courses, researchers and graduate students at King Abdulaziz University were enthused and they interacted and collaborated closely, presenting more than one hundred seminars and lectures, finding many more international connections, visiting high-level researchers while participating actively in conferences. Interestingly, the main topics of their common interest were listed in the National Science, Technology, and Innovation Plan (NSTIP) for the Kingdom of Saudi Arabia (KSA), directed by King Abdulaziz City for Science and Technology (KACST). This motivated the team members to apply for research grants from KACST. Four proposed projects were submitted and all four were recommended and approved. Indeed, one project was highly recommended by KACST. The team members had already drafted a proposal to establish a research group in algebraic structures and its applications. This was approved by the Deanship of Scientific Research at King Abdulaziz University after the importance of these topics and the proposed research directions were recognized. The area of the research group has a strong interaction with the priority science and technology fields in cyber-security, also machine learning and related topics, which are aligned with KSA Vision 2030, as recommended by the International Collaboration Conferences organized by the Research and Development office (RDO) at the Ministry of Education held in Riyadh on April 23-24, 2018.

Location & facilities

The research group finds itself in Room 160 of Building 115 of King Abdulaziz University (main campus), on the ground floor. This laboratory is well-furnished and well-equipped with ten high-performance laptops, two desktop computers, two colour printers, one photocopier machine, a MAGMA (mathematical computer algebra) software license from Sydney University in Australia, and other mathematical application licenses, two smart-boards and two white-boards, the costs of which have been covered in the main by research project grants.

Crash Courses & Seminar Lectures

Six crash courses were organized and given by well-known scientists on the topic of coding theory, cryptography, number theory and ring theory attended by all members and graduate students of the group, with more than one hundred seminar lectures mostly given by students and visitors.

Publications

One book entitled “Codes and Rings: Theory and Practice”. Academic Press, 12 Jun 2017 - Mathematics - 318 pages

Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory.

New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area.