Information on Result #1312098
Linear OA(851, 4109, F8, 14) (dual of [4109, 4058, 15]-code), using 7 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0) based on linear OA(849, 4100, F8, 14) (dual of [4100, 4051, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(849, 4096, F8, 14) (dual of [4096, 4047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(845, 4096, F8, 13) (dual of [4096, 4051, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(80, 4, F8, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 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(851, 4109, F8, 2, 14) (dual of [(4109, 2), 8167, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(851, 4109, F8, 3, 14) (dual of [(4109, 3), 12276, 15]-NRT-code) | [i] | ||
| 3 | Digital (37, 51, 4109)-net over F8 | [i] | ||
| 4 | Linear OOA(851, 2054, F8, 2, 14) (dual of [(2054, 2), 4057, 15]-NRT-code) | [i] | OOA Folding | |