Abstract: Classifications of (v, k, 1) cyclic difference families (CDFs) by other authors are known for k = 3 and v  57, k = 4 and v  64, k = 5 and v  65, k = 6 and v = 91 and k = 7 and v = 91. In this work we construct all inequivalent (v, k, 1) CDFs (respectively all multiplier inequivalent cyclic 2-(v, k, 1) designs) with k  11 and some small v by a computer search and an algorithm similar to the one applied for the classification of optimal orthogonal codes in our previous works. We obtain the same number of inequivalent CDFs for all the parameters, for which previous classification results are known. The new parameters covered by our software for k  7 are (61, 3, 1), (73, 4, 1), (76, 4, 1), (81, 5, 1), and (85, 5, 1) CDFs.

Keywords: cyclic difference set, Steiner triple system, optical orthogonal code

ACM Classification Keywords: Algorithms

Link:

CLASSIFICATION RESULTS FOR (v, k, 1) CYCLIC DIFFERENCE FAMILIES WITH SMALL PARAMETERS

Tsonka Baicheva, Svetlana Topalova

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p02.pdf