Geodesic
Minimum sum and difference covers of abelian groups
Journal of integer sequences, Tome 7 (2004) no. 2
A subset S of a finite Abelian group G is said to be a sum cover of G if every element of G can be expressed as the sum of two not necessarily distinct elements in S , a strict sum cover of G if every element of G can be expressed as the sum of two distinct elements in S , and a difference cover of G if every element of G can be expressed as the difference of two elements in S . For each type of cover, we determine for small k the largest Abelian group for which a k -element cover exists. For this purpose we compute a minimum sum cover, a minimum strict sum cover, and a minimum difference cover for Abelian groups of order up to 85, 90, and 127, respectively, by a backtrack search with isomorph rejection.
Classification : 05B40, 20K01
Keywords: additive base, backtrack search, difference set, covering 
@article{JIS_2004__7_2_a3,
     author = {Haanp\"a\"a,  Harri},
     title = {Minimum sum and difference covers of abelian groups},
     journal = {Journal of integer sequences},
     year = {2004},
     volume = {7},
     number = {2},
     zbl = {1068.11016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2004__7_2_a3/}
}
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Haanpää,  Harri. Minimum sum and difference covers of abelian groups. Journal of integer sequences, Tome 7 (2004) no. 2. http://geodesic.mathdoc.fr/item/JIS_2004__7_2_a3/