Computing
Algebraic
Codes

Introduction
This web site is an interface to a program that allows you compute code parameters for "small" linear Binary Algebraic codes and their various extensions. There is a computational time limit in effect for practical reasons, but if you are interested in coding parameters for a bigger code please feel free to send me e-mail.

Most of the algorithms used for this computation are described in the following documents:

  1. A. Trachtenberg, Designing Lexicographic Codes with a Given Trellis Complexity, IEEE Trans. Inf. Theory, to appear (expected 1/02): available in ps (1.1M), pdf (343k), or html.
  2. A. Trachtenberg, Error-Correcting Codes on Graphs: Lexicodes, Trellises, and Factor Graphs, my Ph.D. thesis from the University of Illinois at Urbana/Champaign, Department of Computer Science: available in html, postscript (1.2M) or pdf (1M).
Related documents are also available on my web page: http://people.bu.edu/trachten.

Contents

  1. Basics
  2. Code Display Options
  3. Post-Processing options
  4. Code Extensions
  5. Submit

Computation
Please enter information about your code:

Basics

 How much computation time do you wish to be allocated to your process?
Computation Time Bound (limited to 99 seconds; e-mail me if you need more):

Starting code (Please describe the starting code explicitly with either a (binary) generator matrix or a parity-check matrix or else, if you check "zero-code", the zero code will be the starting code. The input format of the various matrices should be evident from the default example below).
the zero code
generator matrix
parity-check matrix
(Implementation note: When a parity-check matrix is specified, it may be row-reduced by the program before calculations are made)
Code Display OptionsPost-Processing Options
Display minimum distance (SLOW)
Display covering radius
Display parity-check matrix
Display row-reduced generator matrix
Display Minimum Span Generator Matrix
Display Tanner graph profile
Display trellis complexity profile
Display dual code
No post-processing
Optimal code permutation with respect to decoding complexity (SLOW)
Semi-optimal code permutation with respect to decoding complexity (FASTER)

Compute Code Extensions
No extensions
(For any of the following extensions, you must specify the desired minimum distance of the generated family of codes, as well as the number of extensions to generate) 
Minimum Distance:      Number of extensions:

Lexicographic extension: extension based on adding lexicographically earliest generators
Trellis-oriented lexicographic extension: Version of lexicographic extension which locally optimizes trellis-complexity
State-bounded extension: Codes based on the lexicodes whose trellis state-complexity (logarithm of maximum number of states in the decoding trellis) is bounded by the number:

Submit
Please e-mail me at trachten@bu.edu and/or cite one of the basis papers (mentioned in the beginning of this document) if you find this site useful.

Developed by Ari Trachtenberg.
Graphics furnished by Psyched Up Graphics