The nonexistence of some five-dimensional quaternary linear codes

Abstract

Let n/sub 4/(k, d) be the smallest integer n, such that a quaternary linear [n, k, d; 4]-code exists. It is proved that n/sub 4/(5, 20)=30, n/sub 4/(5, 42)/spl ges/59, n/sub 4/(5, 45)/spl ges/63, n/sub 4/(5, 64)/spl ges/88, n/sub 4/(5, 80)=109, n/sub 4/(5, 140)/spl ges/189, n/sub 4/(5, 143)/spl ges/193, n/sub 4/(5, 168)/spl ges/226, n/sub 4/(5, 180)/spl ges/242, n/sub 4/(5, 183)/spl ges/246, n/sub 4/(5, 187)=251. >