Information on Result #814163
Linear OOA(3150, 9854, F3, 2, 24) (dual of [(9854, 2), 19558, 25]-NRT-code), using OOA 2-folding based on linear OA(3150, 19708, F3, 24) (dual of [19708, 19558, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3150, 19709, F3, 24) (dual of [19709, 19559, 25]-code), using
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 22, F3, 1) (dual of [22, 21, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(19) [i] based on
Mode: Constructive and 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(3150, 9854, F3, 3, 24) (dual of [(9854, 3), 29412, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3150, 9854, F3, 4, 24) (dual of [(9854, 4), 39266, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3150, 9854, F3, 5, 24) (dual of [(9854, 5), 49120, 25]-NRT-code) | [i] | ||
| 4 | Digital (126, 150, 9854)-net over F3 | [i] | ||