Characterization of some minimal codes for secret sharing

Recently, several authors used linear codes to construct secret sharing schemes. It is known that if each nonzero codeword of a code [Formula: see text] is minimal, then the dual code [Formula: see text] is suitable for secret sharing. To seek such codes Ashikhmin–Barg give a sufficient condition from weights; in [Formula: see text] code [Formula: see text], let [Formula: see text] and [Formula: see text] be the minimum and maximum nonzero weights, respectively. If [Formula: see text] then all nonzero codewords of [Formula: see text] are minimal. In this paper, a necessary and sufficient condition is given for self-dual codes and for MDS codes to verify the inequality (*). Special codes are examined and applied for secret sharing schemes.

EXPLICIT DETERMINATION OF CERTAIN MINIMAL ABELIAN CODES AND THEIR MINIMUM DISTANCES

In this paper minimal codes for several classes of non-cyclic abelian groups have been constructed by explicitly determining a complete set of primitive idempotents in the corresponding group algebras. Some classes of non-p-groups have also been considered. The minimum distances of such abelian codes have been discussed and compared to the minimum distances of cyclic codes of same lengths and dimensions over the same field.