Abstract
It has been known for a long time that t-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a t-design. While a lot of progress in the direction of constructing codes from t-designs has been made, only a small amount of work on the construction of t-designs from codes has been done. The objective of this paper is to construct infinite families of 2-designs and 3-designs from a type of binary linear codes with five weights. The total number of 2-designs and 3-designs obtained in this paper are exponential in any odd m and the block size of the designs varies in a huge range.
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Acknowledgements
C. Ding’s research was supported by the Hong Kong Research Grants Council, Proj. No. 16300415.
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Communicated by L. Teirlinck.
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Ding, C. Infinite families of 3-designs from a type of five-weight code. Des. Codes Cryptogr. 86, 703–719 (2018). https://doi.org/10.1007/s10623-017-0352-6
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DOI: https://doi.org/10.1007/s10623-017-0352-6