Information on Result #1313877
Linear OA(1686, 5004, F16, 28) (dual of [5004, 4918, 29]-code), using 898 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 7 times 0, 1, 33 times 0, 1, 117 times 0, 1, 288 times 0, 1, 446 times 0) based on linear OA(1679, 4099, F16, 28) (dual of [4099, 4020, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(1679, 4096, F16, 28) (dual of [4096, 4017, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(1676, 4096, F16, 27) (dual of [4096, 4020, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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 | Linear OOA(1686, 5004, F16, 2, 28) (dual of [(5004, 2), 9922, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (58, 86, 5004)-net over F16 | [i] | ||
| 3 | Linear OOA(1686, 2502, F16, 2, 28) (dual of [(2502, 2), 4918, 29]-NRT-code) | [i] | OOA Folding | |