Information on Result #1313596
Linear OA(1624, 4167, F16, 8) (dual of [4167, 4143, 9]-code), using 66 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 61 times 0) based on linear OA(1622, 4099, F16, 8) (dual of [4099, 4077, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(1622, 4096, F16, 8) (dual of [4096, 4074, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1619, 4096, F16, 7) (dual of [4096, 4077, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(1624, 4167, F16, 2, 8) (dual of [(4167, 2), 8310, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (16, 24, 4167)-net over F16 | [i] | ||
| 3 | Linear OOA(1624, 2083, F16, 2, 8) (dual of [(2083, 2), 4142, 9]-NRT-code) | [i] | OOA Folding | |