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 2 n k ≥ , we can find a set of [ , ] n k disjoint linear codes with cardinality 2no 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.