Cyclic quasi-symmetric designs and self-orthogonal codes of length 63. (English) Zbl 1243.05044
Summary: The enumeration of binary cyclic self-orthogonal codes of length 63 is used to prove that any cyclic quasi-symmetric \(2\)-\((63,15,35)\) design with block intersection numbers \(x=3\) and \(y=7\) is isomorphic to the geometric design having as blocks the three-dimensional subspaces in \(\text{PG}(5,2)\).
MSC:
| 05B05 | Combinatorial aspects of block designs |
| 05B25 | Combinatorial aspects of finite geometries |
| 51E22 | Linear codes and caps in Galois spaces |
| 94B15 | Cyclic codes |
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