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On constructing disjoint linear codes

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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 2n-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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References

  1. Johansson T, Pasalic E. A construction of resilient functions with high nonlinearity. IEEE Transactions on Information Theory, 2003, 49(2): 494–501

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Authors and Affiliations

  1. State Key Laboratory of Intergrated Service Networks, Xidian University, Xi’an, 710071, China

    Zhang Weiguo & Xiao Guozhen

  2. College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, 100022, China

    Cai Mian

Authors
  1. Zhang Weiguo
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  2. Cai Mian
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  3. Xiao Guozhen
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Correspondence to Zhang Weiguo.

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Zhang, W., Cai, M. & Xiao, G. On constructing disjoint linear codes. Front. Comput. Sc. China 1, 226–230 (2007). https://doi.org/10.1007/s11704-007-0023-2

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  • DOI: https://doi.org/10.1007/s11704-007-0023-2

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