A 71-year breakthrough in research 

The first linear code supporting a 4-design is the Golay ternary code with parameters [11, 6, 5] discovered in 1949. The question as to whether there is an infinite family of linear codes holding an infinite family of 4-designs remained open for 71 years.  In 2020, Chunming Tang and Cunsheng Ding settled this long-standing problem by presenting an infinite family of BCH codes of length 22m +1 + 1 over GF(22m +1 ) holding an infinite family of 4-(22m +1 + 1, 6, 22m − 4) designs. Details of this 71-year research breakthrough can be found in the following reference: 

C. Tang, C. Ding, An infinite family of linear codes supporting 4-designs, IEEE Trans. Information Theory 67(1) (2021), 244-254.


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