Infinite families of 2-designs and 3-designs from linear codes |
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Authors: | Cunsheng Ding Chengju Li |
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Institution: | 1. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China |
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Abstract: | The interplay between coding theory and -designs started many years ago. While every -design yields a linear code over every finite field, the largest for which an infinite family of -designs is derived directly from a linear or nonlinear code is . Sporadic -designs and -designs were derived from some linear codes of certain parameters. The major objective of this paper is to construct many infinite families of -designs and -designs from linear codes. The parameters of some known -designs are also derived. In addition, many conjectured infinite families of -designs are also presented. |
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Keywords: | Difference family Cyclic code Linear code |
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