On codes meeting the Griesmer bound.
The main results in this paper are the following two theorems: Theorem 9. Let \(s+t<q\) and \(k\geq4\). Each \([g_q(k,d),k,d]_q\) code with \[ sq^{k-1}-(s+t)q^{k-2}-q^{k-4}\leq d<sq^{k-1}-(s+t)q^{k-2} \] can be extended to a \([g_q(k,d'),k,d']_q\) code with \(d'=sq^{k-1}-(s+t)q^{k-2}\). Theorem 12. If \((s+t)^2+3(s+t)+1\leq q\), then each \([g_q(k,d),k,d]_q\) code with \[ sq^{k-1}-(s+t)q^{k-2}-q^{k-3}+1\leq d< sq^{k-1}-(s+t)q^{k-2} \] and \(k\geq3\) can be extended to a \([g_q(k,d'),k,d']_q\) code with \(d'=sq^{k-1}-(s+t)q^{k-2}\).
scientific article; zbMATH DE number 2032868