A CONSTRUCTION OF SOME [N, K, D Q]-CODES MEETING THE GRIESMER BOUND

Let [n, k, d, q]-code denote a q-ary linear code, with length n, dimension k and minimum distance d. Griesmer's bound is well known as a lower bound on n for given integers k, d and q. Linear codes meeting the Griesmer bound are called optimal linear codes. This paper is a survey on the construction of optimal linear codes. Some relations among optimal linear codes, linear programming, maxhypers and minihypers are investigated. Maxhypers and minihypers are very useful in obtaining and characterizing optimal linear codes. Furthermore, we present many optimal linear codes which are constructed using these relations and l intersectional empty sets.