On Optimal Linear Codes over F8

  • Rie Kanazawa
  • Tatsuya Maruta

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=0d/8i for all d833. As a continuation of Jones et al. [Electronic J. Combinatorics 13 (2006), #R43], we determine n8(4,d) for 117 values of d with 113d832 and give upper and lower bounds on n8(4,d) for other d using geometric methods and some extension theorems for linear codes.

Published
2011-02-14
Article Number
P34