Some bounds on the size of codes

TL;DR

This paper introduces new upper bounds on the size of non-linear, systematic, and linear codes that outperform existing bounds in many cases, offering improved theoretical limits for code design.

Contribution

The paper presents novel upper bounds on code sizes that are independent of traditional bounds and improve upon previous bounds by Litsyn and Laihonen.

Findings

Our bounds often outperform existing bounds in various cases.

The bounds are applicable to non-linear, systematic, and linear codes.

Experimental results demonstrate the superiority of our bounds in many scenarios.

Abstract

We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the Plotkin bound, and one of these is actually an improvement of a bound by Litsyn and Laihonen. Our experiments show that in some cases (the majority of cases for some q) our bounds provide the best value, compared to all other theoretical bounds.