Information on Result #2172216
There is no linear OA(1665, 111, F16, 61) (dual of [111, 46, 62]-code), because 3 times truncation would yield linear OA(1662, 108, F16, 58) (dual of [108, 46, 59]-code), but
- construction Y1 [i] would yield
- OA(1661, 65, S16, 58), but
- the linear programming bound shows that M ≥ 159214 122701 309768 707410 104386 945873 298246 228915 255775 554254 178010 880553 254912 / 5487 > 1661 [i]
- linear OA(1646, 108, F16, 43) (dual of [108, 62, 44]-code), but
- discarding factors / shortening the dual code would yield linear OA(1646, 97, F16, 43) (dual of [97, 51, 44]-code), but
- construction Y1 [i] would yield
- OA(1645, 49, S16, 43), but
- the linear programming bound shows that M ≥ 79 689768 125026 220634 634045 411816 077548 174434 353547 313152 / 47 > 1645 [i]
- linear OA(1651, 97, F16, 48) (dual of [97, 46, 49]-code), but
- discarding factors / shortening the dual code would yield linear OA(1651, 68, F16, 48) (dual of [68, 17, 49]-code), but
- residual code [i] would yield OA(163, 19, S16, 3), but
- 1 times truncation [i] would yield OA(162, 18, S16, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 271 > 162 [i]
- 1 times truncation [i] would yield OA(162, 18, S16, 2), but
- residual code [i] would yield OA(163, 19, S16, 3), but
- discarding factors / shortening the dual code would yield linear OA(1651, 68, F16, 48) (dual of [68, 17, 49]-code), but
- OA(1645, 49, S16, 43), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(1646, 97, F16, 43) (dual of [97, 51, 44]-code), but
- OA(1661, 65, S16, 58), but
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.