Klaus Huber (University of Illinois / Deutsche Telekom):
Applications of Fermat's Two Squares Theorem in Information Technology
Fermat's Two Squares Theorem tells us that any prime p of the form
p = 1 mod 4 can essentially be written uniquely as sum of two
squares, i.e. p=a a + b b. This theorem is the
background for the three applications given in the talk. The first
is an application in channel coding. A metric called Mannheim
metric is treated and it is anticipated that once decoders
for more than two errors in this metric are available, algebraic
codes using this metric will be important. The second
application is related to complex convolutions using surrogate
fields and the third treats a public key knapsack system.