Information on Result #1312108
Linear OA(856, 4162, F8, 15) (dual of [4162, 4106, 16]-code), using 59 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 51 times 0) based on linear OA(853, 4100, F8, 15) (dual of [4100, 4047, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(853, 4096, F8, 15) (dual of [4096, 4043, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(856, 4162, F8, 2, 15) (dual of [(4162, 2), 8268, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(856, 4162, F8, 3, 15) (dual of [(4162, 3), 12430, 16]-NRT-code) | [i] | ||
| 3 | Digital (41, 56, 4162)-net over F8 | [i] | ||
| 4 | Linear OOA(856, 2081, F8, 2, 15) (dual of [(2081, 2), 4106, 16]-NRT-code) | [i] | OOA Folding | |