Information on Result #1313639
Linear OA(1639, 4115, F16, 13) (dual of [4115, 4076, 14]-code), using 14 step Varšamov–Edel lengthening with (ri) = (2, 13 times 0) based on linear OA(1637, 4099, F16, 13) (dual of [4099, 4062, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(1637, 4096, F16, 13) (dual of [4096, 4059, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1634, 4096, F16, 12) (dual of [4096, 4062, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(1639, 4115, F16, 2, 13) (dual of [(4115, 2), 8191, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (26, 39, 4115)-net over F16 | [i] | ||
| 3 | Linear OOA(1639, 2057, F16, 2, 13) (dual of [(2057, 2), 4075, 14]-NRT-code) | [i] | OOA Folding | |