Chunlei Li is the second COINS student who has graduated this year. The thesis defense took place at the University of Bergen on Monday 16th of June. Title of the dissertation: “Sequences and Linear Codes from Highly Nonlinear Functions”. The dissertation itself can be found by following the link.
In digital communication data is represented with ones and zeros (binary form). Binary sequences that have good properties are essential to increase robustness and reduce likelihood of errors in modern communication systems. Whole family of binary sequences with good mutual “correlation properties” is used in modern CDMA systems. Such sequences can also be used to construct error correcting codes. They correct errors that occur during transmission (or storage) of data that is susceptible to noise. The binary sequences also have many important applications in cryptography and are therefore of great importance for achieving secure and reliable communications.
A fundamental problem is to construct families of good sequences. A method for constructing both sequence families, error correcting codes and cryptographic systems, with desired properties is by using non-linear functions. The thesis studies special classes of “perfect” (PN) or “almost perfect” (APN) non-linear functions and shows how these features can be used to create new sequence families and classes of codes with optimal error correcting properties. A mathematical analysis of the new sequence families and codes which were constructed in the study shows promising results.