Results on Binary Linear Codes With Minimum Distance 8 and 10
Information Theory
2016-11-18 v1 math.IT
Abstract
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact bounds for binary linear codes. Primarily two algorithms considering the dual codes are used, namely extension of dual codes with a proper coordinate, and a fast algorithm for finding a maximum clique in a graph, which is modified to find a maximum set of vectors with the right dependency structure.
Cite
@article{arxiv.1006.0109,
title = {Results on Binary Linear Codes With Minimum Distance 8 and 10},
author = {Iliya Bouyukliev and Erik Jakobsson},
journal= {arXiv preprint arXiv:1006.0109},
year = {2016}
}
Comments
Submitted to the IEEE Transactions on Information Theory, May 2010 To be presented at the ACCT 2010