Information on Result #547664
There is no linear OA(1617, 48, F16, 16) (dual of [48, 31, 17]-code), because dual of a near-MDS code is again a near-MDS code would yield linear OA(1631, 48, F16, 30) (dual of [48, 17, 31]-code), but
- discarding factors / shortening the dual code would yield linear OA(1631, 34, F16, 30) (dual of [34, 3, 31]-code), 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(1618, 49, F16, 17) (dual of [49, 31, 18]-code) | [i] | Truncation | |
| 2 | No linear OA(1619, 50, F16, 18) (dual of [50, 31, 19]-code) | [i] | ||
| 3 | No linear OA(1620, 51, F16, 19) (dual of [51, 31, 20]-code) | [i] | ||
| 4 | No linear OA(1621, 52, F16, 20) (dual of [52, 31, 21]-code) | [i] | ||
| 5 | No linear OA(1622, 53, F16, 21) (dual of [53, 31, 22]-code) | [i] | ||
| 6 | No linear OA(1623, 54, F16, 22) (dual of [54, 31, 23]-code) | [i] | ||
| 7 | No linear OA(1624, 55, F16, 23) (dual of [55, 31, 24]-code) | [i] | ||
| 8 | No linear OA(1625, 56, F16, 24) (dual of [56, 31, 25]-code) | [i] | ||
| 9 | No linear OA(1626, 57, F16, 25) (dual of [57, 31, 26]-code) | [i] | ||
| 10 | No linear OA(1627, 58, F16, 26) (dual of [58, 31, 27]-code) | [i] | ||
| 11 | No linear OA(1628, 59, F16, 27) (dual of [59, 31, 28]-code) | [i] | ||
| 12 | No linear OA(1629, 60, F16, 28) (dual of [60, 31, 29]-code) | [i] | ||
| 13 | No linear OA(1630, 61, F16, 29) (dual of [61, 31, 30]-code) | [i] | ||
| 14 | No linear OOA(1618, 48, F16, 2, 17) (dual of [(48, 2), 78, 18]-NRT-code) | [i] | m-Reduction for OOAs | |
| 15 | No linear OOA(1619, 48, F16, 2, 18) (dual of [(48, 2), 77, 19]-NRT-code) | [i] | ||
| 16 | No linear OOA(1620, 48, F16, 2, 19) (dual of [(48, 2), 76, 20]-NRT-code) | [i] | ||
| 17 | No linear OOA(1621, 48, F16, 2, 20) (dual of [(48, 2), 75, 21]-NRT-code) | [i] | ||
| 18 | No linear OOA(1622, 48, F16, 2, 21) (dual of [(48, 2), 74, 22]-NRT-code) | [i] | ||
| 19 | No linear OOA(1623, 48, F16, 2, 22) (dual of [(48, 2), 73, 23]-NRT-code) | [i] | ||
| 20 | No linear OOA(1624, 48, F16, 2, 23) (dual of [(48, 2), 72, 24]-NRT-code) | [i] | ||
| 21 | No linear OOA(1625, 48, F16, 2, 24) (dual of [(48, 2), 71, 25]-NRT-code) | [i] | ||
| 22 | No linear OOA(1626, 48, F16, 2, 25) (dual of [(48, 2), 70, 26]-NRT-code) | [i] | ||
| 23 | No linear OOA(1627, 48, F16, 2, 26) (dual of [(48, 2), 69, 27]-NRT-code) | [i] | ||
| 24 | No linear OOA(1628, 48, F16, 2, 27) (dual of [(48, 2), 68, 28]-NRT-code) | [i] | ||
| 25 | No linear OOA(1629, 48, F16, 2, 28) (dual of [(48, 2), 67, 29]-NRT-code) | [i] | ||
| 26 | No linear OOA(1630, 48, F16, 2, 29) (dual of [(48, 2), 66, 30]-NRT-code) | [i] | ||
| 27 | No linear OOA(1617, 48, F16, 2, 16) (dual of [(48, 2), 79, 17]-NRT-code) | [i] | Depth Reduction | |
| 28 | No digital (1, 17, 48)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |