Euclidean Spaces with Hamming Mininorm

Abstract

A mininorm  on  a  vector  space  X over  the  field   or   is a function w from X to  satisfying the properties of a norm || || with the property ||αx|| = |α| ||x||, α ∈ , x ∈ X replaced by the following property: ||αx|| = ||x||  for all x ∈ X,  . There are several mininorms on the Euclidean spaces  k . One such mini- norm is the Hamming weight function. In this paper, we discuss certain basic properties of Euclidean spaces with the Hamming mininorm and also some structural properties of these spaces. Mathematic Subject Calssification 2010: 46B99, 46A19