English

An improvement of the asymptotic Elias bound for non-binary codes

Information Theory 2018-02-28 v3 math.IT

Abstract

For non-binary codes the Elias bound is a good upper bound for the asymptotic information rate at low relative minimum distance, where as the Plotkin bound is better at high relative minimum distance. In this work, we obtain a hybrid of these bounds which improves both. This in turn is based on the anticode bound which is a hybrid of the Hamming and Singleton bounds and improves both bounds. The question of convexity of the asymptotic rate function is an important open question. We conjecture a much weaker form of the convexity, and we show that our bounds follow immediately if we assume the conjecture.

Keywords

Cite

@article{arxiv.1705.07785,
  title  = {An improvement of the asymptotic Elias bound for non-binary codes},
  author = {Krishna Kaipa},
  journal= {arXiv preprint arXiv:1705.07785},
  year   = {2018}
}

Comments

To appear in IEEE Transactions on Information Theory. Appendix section has been revised