ALGEBRAIC ASPECTS OF DIGITAL COMMUNICATIONS
Tony Shaska, M. Qarri · Albanian Journal of Mathematics · 2008
Developments of the last few decades in digital communications have created a close link between mathematics and areas of computer science and electrical engineering.A collaboration between such areas now seems very natural due to problems which require deep knowledge and expertise in each area.A special role in such collaboration has played algebra and some of its branches such as algebraic geometry, computational algebra, group theory, etc.As a result of such cooperation now we have disciplines such as coding theory and cryptography which are considered a mix of mathematics, computer science, and electrical engineering.Coding theory is one of the most important and direct applications of information theory.It is a branch of electrical engineering, digital communication, mathematics, and computer science designing ecient and reliable data transmission methods, so that redundancy in the data can be removed and errors induced by a noisy channel can be corrected.It started with Shannon, Hamming, and many others in the mid 20-th century and became one of the most active areas of research for most of the second half of the 20-th century.Algebraic coding theory was the main direction of coding theory, even though recently other ways of coding have been developed.For more details in coding theory a wonderful source is [2] among many other publications.Cryptology, is the science of hiding information, and historically has received much attention from the public.As a science was also put in solid background in the second half of the 20-th century.It is a mixture of theoretical mathematics and computer science which focuses more in areas such as number theory, algebraic geometry, graph theory, algorithm analysis, etc.There have been many conferences and publications which have explored the common ground among such areas; some of the more recent ones are [6,7].