Citation

Abstract

The Griesmer bound is a classical technique (developed in 1960) for estimating the minimum length n required for a binary linear code with a given dimension k and minimum distance d. In this article, a unified derivation of the Griesmer bound and two new variations on it are presented. The first variation deals with linear codes which contain the all-ones vector; such codes are quite common and are useful in practice because of their “transparent” properties. The second variation deals with codes that are constrained to contain a word of weight > M. In both cases these constraints (the all-ones word or a word of high weight) can increase the minimum length of a code with given k and d.

Details

Volume
42-105
Published
May 15, 1991
Pages
41–44
File Size
173.7 KB