English

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.

Keywords

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

R2 v1 2026-06-21T15:30:25.092Z