Modifications of the Griesmer bound

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 greater than or equal to 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.