On constructing disjoint linear codes

doi:10.1007/s11704-007-0023-2

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Front. Comput. Sci. ›› 2007, Vol. 1 ›› Issue (2) : 226-230. DOI: 10.1007/s11704-007-0023-2

On constructing disjoint linear codes

ZHANG Weiguo¹, ZHANG Weiguo¹, XIAO Guozhen¹, XIAO Guozhen¹, CAI Mian², CAI Mian²

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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.

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ZHANG Weiguo, ZHANG Weiguo, XIAO Guozhen, XIAO Guozhen, CAI Mian, CAI Mian. On constructing disjoint linear codes. Front. Comput. Sci., 2007, 1(2): 226‒230 https://doi.org/10.1007/s11704-007-0023-2