Note: This document and the projects described in it are property of Gauss Research Foundation, Inc., and are subject to its intellectual property rights.

Research areas

The Gauss Research Foundation is currently working with two main areas of interest related to its Research focus area. The pipeline follows different stages in the Research process. We have established two basic Research levels: Abstract Research and Applied Research.

Abstract research:

  1. Algebraic number theory: The study of exponential sums and their bounds. In this area we have improved on bounds, of Deligne, Weil and Ax-Katz. We have applied the research to the study of error correcting codes, their parameters and weight enumeration.
  2. Algebraic geometry and its application to coding theory including the study of algebraic geometric Goppa codes.
  3. Study of finite fields.

Applied research:

  1. Study of error correcting codes, public key cryptography and computational number theory.
  2. Design of sequences with good correlation with applications to :
    • One and multiple target recognition (Costas and Sonar sequences included).
    • Study of optical CDMA as well as classical CDMA.
    • Watermarking.
  3. Application of error correcting to genetic networks.
  4. Efficient computer searches using high performance computers, such as parallel computers.
  5. Some of the main results obtained in the above area: (the research has been awarded an IEEE fellowship):
    • Developed a p-adic serre bound.
    • Development on the Moreno-Moreno p-adic bounds that gives improvements to the Chevalley-Warning and Ax-Katz result.
    • Solution to several research problems of MacWilliams and Sloanne.
    • Proof of Golomb conjecture D, as well as conjecture A. The second conjecture was obtained using computations as well as theory.
  6. Internet Governance for the ccTLD’s in the Caribbean Region

    Internet governance is the development and application by Governments, the private sector and civil society, in their respective roles, of shared principles, norms, rules, decision-making procedures, and programs that shape the evolution and use of the Internet. The World Summit Information Society, a division created by the United Nations to develop and establish the foundations for an Information Society for all, reflecting all the different interests at stake, divided Internet Governance in four sections:

    • Infrastructure (mainly the Domain Name System and IP addresses)
    • Internet issues such as security, safety and privacy (including spam and cybercrime)
    • Intellectual property and international trade (including copyrights)
    • Development Issues (particularly developing countrie

Following these guidelines, Gauss Research Foundation has created an area dedicated to the development of the Caribbean region for Internet Governance, Science and technology research, Information Society as well the support of prospective students in these areas. We have been present in important meetings such as:

Grenada 1st IGF Forum, where we also acted as facilitator for the workshops, Anguilla Meeting for Caribbean Ministers, Curacao 4th IGF Forum, Haiti 5th IGF Forum and Barbados Meeting for Caribbean Ministers.

Our continued active participation denotes our commitment with the Caribbean region and Puerto Rico, to prepare our countries to face this new Era of Information Society.