Lay summary
Coding theory has emerged out of the need for better communication and
has rapidly developed as a mathematical theory in strong relationship
with algebra, combinatorics and algebraic geometry. Nowadays
error-correcting-codes are used in everyday practical applications
such as digital-storage media, wire-line and wireless networks, and
satellite and deep-space communication systems. Example of simple
block codes are the international standard book numbers (ISBN), the
ASCII code and various encoding schemes used to identify bank
accounts. Network coding theory is concerned with the encoding and
transmission of information where there may be many information
sources and possibly many receivers. R. Koetter and F. Kschischang
identified a fundamental mathematical question which lies at the heart
of network coding. This formulation seeks the construction of good
subsets of the finite Grassmann variety and it is the intended plan of
the proposed research to use algebraic techniques to come up with new
network codes which have better throughput and efficient decoding.
In the center of the mathematical interest will be the study of orbit
codes, a concept introduced by the PI and his coauthors while supported
by SNF grant Project no. 126948.