On Optimal Linear Codes over F8
Abstract
Let nq(k,d) be the smallest integer n for which there exists an [n,k,d]q code for given q,k,d. It is known that n8(4,d)=∑3i=0⌈d/8i⌉ for all d≥833. As a continuation of Jones et al. [Electronic J. Combinatorics 13 (2006), #R43], we determine n8(4,d) for 117 values of d with 113≤d≤832 and give upper and lower bounds on n8(4,d) for other d using geometric methods and some extension theorems for linear codes.