کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4649604 | 1342461 | 2009 | 5 صفحه PDF | دانلود رایگان |

Generalized Steiner systems GS(2,k,v,g) were first introduced by Etzion and used to construct optimal constant weight codes over an alphabet of size g+1g+1 with minimum Hamming distance 2k−32k−3, in which each codeword has length vv and weight kk. As to the existence of a GS(2,k,v,g), a lot of work has been done for k=3k=3, while not so much is known for k=4k=4. The notion k-∗k-∗GDD was first introduced by Chen et al. and used to construct GS(2,3,v,6). The necessary condition for the existence of a 4-∗GDD(6v) is v≥14v≥14. In this paper, it is proved that there exists a 4-∗GDD(6v) for any prime power v≡3,5,7(mod8) and v≥19v≥19. By using this result, the known results on the existence of optimal quaternary constant weight codes are then extended.
Journal: Discrete Mathematics - Volume 309, Issue 20, 28 October 2009, Pages 6009–6013