Minimal linear codes from Maiorana-McFarland functions

Minimal linear codes have important applications in secret sharing schemes and secure multi-party computation, etc. In this paper, we study the minimality of a kind of linear codes over GF(p) from Maiorana-McFarland functions. We first obtain a new sufficient condition for this kind of linear codes to be minimal without analyzing the weights of its codewords, which is a generalization of some works given by Ding et al. in 2015. Using this condition, it is easy to verify that such minimal linear codes satisfy w(min)/w(max) <= P-1/p for any prime p, where w(min) and w(maz) denote the minimum and maximum nonzero weights in a code, respectively. Then, by selecting the subsets of GF(p)(s), we present two new infinite families of minimal linear codes with w(min)/w(max) <= P-1/p for any prime p. In addition, the weight distributions of the presented linear codes are determined in terms of Krawtchouk polynomials or partial spreads. (C) 2020 Elsevier Inc. All rights reserved.