Abstract
This paper gives a construction of group divisible designs (GDDs) on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which consist of the error patterns whose first syndromes are zeros recognized from the decoding of binary quadratic residue codes. A conjecture is proposed for this construction of GDDs with larger block sizes.
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Acknowledgements
This research is supported by the Ministry of Science and Technology, Taiwan, ROC under the Projects MOST 103-2632-M-214-001-MY3 including its Subproject MOST 104-2811-M-214-001, and MOST 105-2221-E-214-005.
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Communicated by V. D. Tonchev.
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Lee, CD., Chang, Y. & Liu, Ca. A construction of group divisible designs with block sizes 3 to 7. Des. Codes Cryptogr. 86, 1281–1293 (2018). https://doi.org/10.1007/s10623-017-0395-8
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DOI: https://doi.org/10.1007/s10623-017-0395-8