Optimal Four-Dimensional Codes over GF(8)

Abstract

We prove the nonexistence of several four-dimensional codes over GF(8) that meet the Griesmer bound. The proofs use geometric methods based on the analysis of the weight structure of subcodes. The specific parameters of the codes ruled out are: $[111,4,96],\,$ $[110,4,95],\,$ $[102,4,88],\,$ $[101,4,87],\,$ $[93,4,80],\,$ and the sequence $[29-j,4,24-j]$, for $j=0,1,2$.