Coding Theory and Cryptography, July 21, 2007,
Oakland University, Rochester, MI, USA


Applications of Computer Algebra, ACA 07
July 19-22, 2007

Organizers:

Overview: Coding theory and cryptography have become increasingly important in technology and communication. The goal of this session is to bring together researchers in all aspects of coding theory, cryptography and related areas and to explore the use of computational algebra in such areas.


Topics: They include, but are not limited to:

  • error-correcting codes, 
  • decoding algorithms, related combinatorial problems,
  • cyclic codes, BCH, and Reed-Solomon codes
  • theta functions, lattices, and codes
  • algebraic curves and AG-codes
  • polynomial methods in coding theory
  • Groebner bases and codes
  • low density codes
  • quantum codes

and many others. If you are planning to attend please send us a title and abstract. We would like to accomodate as many good quality talks as possible.

  • Morning session: 9am-12 noon, Saturday.
  • Afternoon session: 2pm-5pm, Saturday.

Talks:

Shayne Vargo, Michael E. O'Sullivan

San Diego State Univ.

Convergence of the sum-product algorithm on some small graphs.

Abstract
9-9:50am.

David Joyner

USNA

Computational aspects of Duursma zeta functions using SAGE

Abstract
10-10:25am

Jon-Lark Kim

University of Louisville

Remarks on s-extremal codes

10:30-10:55am

S. Wijesiri

Oakland University

Codes over rings of size four, Hermitian lattices, and their corresponding theta functions.

11-11:25am

Cary Huffman

Loyola University Chicago

Additive Cyclic Codes over F4

Abstract
2-2:50pm.

Caleb Shor

Bates College

Codes over Fp2 and Fp x Fp lattices, and theta functions

Abstract
3-3:25pm

Bill Bauldry and Mitchell Carr

Appalachian State University

Structure in the Key Schedule of AES  

Abstract
3:30-3:55

Vladimir D. Tonchev

Algorithms for optimal comma-free codes

4-4:25pm






Abstracts:

  1. Cary Huffman, Additive cyclic codes over F4  

    We examine the structure of additive cyclic codes over F4 of odd length n. We provide a canonical decompostion of these codes that allows us to do a number of things. For example, we can show that every such code can be generated by at most two codewords and their cyclic shifts; one codeword will not always suffice. We can also construct and count all such codes. The count depends only on the sizes of the 2-cyclotomic cosets modulo n. We can also construct and count all self-orthogonal and self-dual additive cyclic codes under the trace inner product.

  2. William C Bauldry and Mitchell Carr, Structure in the Key Schedule of AES

    We outline the Advanced Encryption System (AES or Rijndael) which is based on GF(28). Then we look at the key schedule used in AES and display an apparent structure. Last we offer a metric that appears to signal potentially weak keys.

  3. David Joyner, Computational aspects of Duursma zeta functions using SAGE

    Motivated by analogies with local class field theory for function fields, Iwan Duursma introduced the zeta function ZC associated to a linear code C over a finite field. This talk discusses their proprties (conjectural and proven) and some computational methods using the computer algebra system SAGE.

  4. Caleb Shor, Codes over Fp2 and Fp x Fp lattices, and theta functions

    For any linear code C over Fp2 or Fp x Fp and any square-free integer m>0, there is an associated lattice Lm(C) over the ring of integers of a quadratic imaginary extension of Q. The theta functions thetaLm(C) of such lattices are known to determine the symmetrized weight enumerator swe(C) for small primes p = 2, 3. In this talk, we will look at properties of these theta functions that hold for any prime p.

  5. Shayne Vargo and Michael O' Sullivan, Convergence of the Sum-Product Algorithm On Single-Cycle Graphs

    We first introduce a more general version of the Sum-Product Algorithm. We briefly examine how this affects the convergence of trees. Then, we move on to the simple 2-cycle and extend this to cycles of any length. Finally, this generalized SPA allows us to simplify the analysis of any graph containing exactly one cycle to that for an equivalent simple cycle.



Created by Tony Shaska. Last updated 7-11-2007 by David Joyner.