On constructing disjoint linear codes

Abstract

To produce a highly nonlinear resilient function, the disjoint linear codes were originally proposed by Johansson and Pasalic in IEEE Trans. Inform. Theory, 2003, 49(2): 494-501. In this paper, an effective method for finding a set of such disjoint linear codes is presented. When n ≥ 2k , we can find a set of [n,k] disjoint linear codes with cardinality 2^{n -k} + [(n-k)/k]; When n < 2k, no set of disjoint linear codes exists with cardinality at least 2. We also describe a result on constructing a set of [n, k] disjoint linear codes with minimum distance at least some fixed positive integer.

Keywords

cryptography, resilient function, linear code, disjoint linear codes