On the minimum length of quaternary linear codes of dimension five (Q1301710)

Let \(n_q(k,d)\) denote the smallest length of a linear code of length \(n\), dimension \(k\) and minimum distance \(d\). This paper proves the nonexistence of quaternary codes with parameters \([n,k,d]\) being one of \([190,5,141]\), \([239,5,178]\), \([275,5,205]\), \([288,5,215]\), \([291,5,217]\), or \([488,5,365]\). This leads to improved lower bounds for \(n_4(5,d)\) for \(d=141, 142\) and determines the precise value of \(n_4(5,d)\) for \(d=178, 205, 206, 215, 217, 218, 365, 366, 367, 368\). The paper also presents an updated table of \(n_4(5,d)\).