On the Griesmer bound for nonlinear codes
Information Theory
2015-02-27 v1 Combinatorics
math.IT
Abstract
Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound, holds only in the linear case. In this paper we characterize a family of systematic nonlinear codes for which the Griesmer bound holds. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by showing explicit counterexamples. On the other hand, we are also able to provide (weaker) versions of the Griesmer bound holding for all systematic codes.
Keywords
Cite
@article{arxiv.1502.07379,
title = {On the Griesmer bound for nonlinear codes},
author = {Emanuele Bellini and Eleonora Guerrini and Alessio Meneghetti and Massimiliano Sala},
journal= {arXiv preprint arXiv:1502.07379},
year = {2015}
}