5-DESIGN AND COUNTER 5-DESIGN IN THE BINARY GOLAY CODE OF LENGTH 24

Abstract

A close relationship between the coding theory and the design theory has been studied by many researchers. The principal concern is directed to the designs formed by minimal weight code-words or very small weight codewords. In the present article we study more designs. We extend the concept of the incidence relation, one of which is a classical one and the other is a dual one to the classical one in a certain sense. In the present article we focus on the binary Golay code of length 24. But the idea will be applied to a wide class of self-dual codes such as self-dual extremal binary codes or self-dual extremal ternary codes.