Computing
Algebraic
Codes v.2

Introduction

 This web interface allows you to parameters of some small error-correcting codes; the codes must be binary and linear, and there is a computational time limit in effect (if you need parameters for bigger codes, download the related i686 executable or e-mail me.

Background and explanation of algorithms for this computation are described in the following documents:

  1. A. Trachtenberg, Designing Lexicographic Codes with a Given Trellis Complexity, IEEE Trans. Inf. Theory, January 2002: available in ps, pdf, 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 or pdf.
Related documents are also available on my web page, and I would appreciate a citation to one of the IEEE paper above if you make use of this page.

Contents

  1. Basics
  2. Advanced options
    1. Code Display
    2. Post-Processing
    3. Extensions
  3. Submit request

Code information

Basics

 Please provide the initial code explicitly with either a (binary) generator matrix or a parity-check matrix (alternatively, you may select the "zero-code"). The input format should be evident from the default example below.
generator matrix
parity-check matrix
the zero code

Advanced options

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 for decoding complexity (SLOW)
Semi-optimal code permutation for 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 is bounded 2 to the power:

Submit
Please e-mail me at trachten@bu.edu and/or cite the IEEE paper if you find this site useful.

Developed by Ari Trachtenberg.
Graphics furnished by Psyched Up Graphics.