Information on Result #1313923
Linear OA(1694, 4784, F16, 31) (dual of [4784, 4690, 32]-code), using 679 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 20 times 0, 1, 76 times 0, 1, 210 times 0, 1, 364 times 0) based on linear OA(1688, 4099, F16, 31) (dual of [4099, 4011, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(1688, 4096, F16, 31) (dual of [4096, 4008, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(1685, 4096, F16, 30) (dual of [4096, 4011, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(1694, 4784, F16, 2, 31) (dual of [(4784, 2), 9474, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (63, 94, 4784)-net over F16 | [i] | ||
| 3 | Linear OOA(1694, 2392, F16, 2, 31) (dual of [(2392, 2), 4690, 32]-NRT-code) | [i] | OOA Folding | |