Information on Result #586109
There is no linear OOA(2158, 210, F2, 5, 75) (dual of [(210, 5), 892, 76]-NRT-code), because 3 times depth reduction would yield linear OOA(2158, 210, F2, 2, 75) (dual of [(210, 2), 262, 76]-NRT-code), but
- 1 step m-reduction [i] would yield linear OA(2157, 210, F2, 74) (dual of [210, 53, 75]-code), but
- construction Y1 [i] would yield
- linear OA(2156, 190, F2, 74) (dual of [190, 34, 75]-code), but
- construction Y1 [i] would yield
- linear OA(2155, 178, F2, 74) (dual of [178, 23, 75]-code), but
- adding a parity check bit [i] would yield linear OA(2156, 179, F2, 75) (dual of [179, 23, 76]-code), but
- OA(234, 190, S2, 12), but
- discarding factors would yield OA(234, 154, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 17486 314616 > 234 [i]
- discarding factors would yield OA(234, 154, S2, 12), but
- linear OA(2155, 178, F2, 74) (dual of [178, 23, 75]-code), but
- construction Y1 [i] would yield
- OA(253, 210, S2, 20), but
- discarding factors would yield OA(253, 182, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 9064 436853 738748 > 253 [i]
- discarding factors would yield OA(253, 182, S2, 20), but
- linear OA(2156, 190, F2, 74) (dual of [190, 34, 75]-code), but
- construction Y1 [i] would yield
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.