Classification of a class of A3MDS code and applications in secret-sharing schemes

Abstract

A [Formula: see text]-ary linear [Formula: see text] code [Formula: see text] is known as [Formula: see text] code. If [Formula: see text] the code is called a maximum distance separable code. [Formula: see text] codes are known to be useful in the secret-sharing schemes and coding theory. In this paper, we classify all binary self-orthogonal [Formula: see text] codes. We have introduced a subclass of [Formula: see text] codes, called [Formula: see text] codes, to form a special type of secret-sharing scheme where for any participant, there exist [Formula: see text] other participants who can collectively reveal the secret by combining their shares and there exists another set of [Formula: see text] participants including the given participant, who cannot reveal the secret.