Optimal non-projective linear codes constructed from down-sets

Abstract

By an optimal linear code we mean that it has the highest minimum distance with a prescribed length and dimension. We construct several families of optimal linear codes over the finite field IFp by making use of down-sets generated by one maximal element of IFP. "Moreover, we show that these families of optimal linear codes are minimal and contain relative two-weight linear codes, and have applications to secret sharing schemes and wire-tap channel of type II with the coset coding scheme, respectively. (C) 2018 Elsevier B.V. All rights reserved.