A construction of group divisible designs with zero block sum
  This paper gives a construction of group divisible designs on the binary extension fields with block sizes 3, 4, 5, 6, and 7, respectively, which is motivated from the decoding of binary quadratic residue codes. A conjecture is proposed for this construction of group divisible designs with larger block sizes. 
Chong-Dao Lee, Yaotsu Chang, Chia-an Liu
math.CO