Three Approaches to Self-Dual Code Construction
Megan Armentrout, Meagan Pitluck, Ranjan Rohatgi, Joseph Thomas, Selin Kalaycioglu, Klaus M. Lux · 2008
In this paper, we investigate experimental, systematic, and probabalistic approaches to the construction of self-dual codes. After a brief overview of pertinent theory, we first examine Philippe Gaborit and Ayoub Otmani’s experimental method for finding “good” self-dual codes over finite fields, particularly over GF (2) and GF (3). We find that their method effectively obtains “good” self-dual codes of length 2n and consider the theoretical reasons for the procedure’s success. Specifically, we consider the action of orthogonal matrix groups on self-dual codes described by Gerald J. Janusz in “Parametrization of self-dual codes by orthogonal matrices.” Based on this theory, we construct and analyze two group theoretical approaches to computing “good” self-dual codes.