Classification of Linear Codes by Extending Their Residuals

摘要

An approach for classification of linear codes with given parameters starting from their proper residual codes or subcodes is presented. The base of the algorithm is the concept of canonical augmentation which is important for parallel implementations. The algorithms are implemented in the programs LENGTHEXTENSION and DIMEXTENSION of the package QEXTNEWEDITION. As an application, the nonexistence of binary [41, 14,14] codes is proved.