Information on Result #1305101
Linear OA(3169, 838, F3, 41) (dual of [838, 669, 42]-code), using 94 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 9 times 0, 1, 13 times 0, 1, 16 times 0, 1, 18 times 0, 1, 20 times 0) based on linear OA(3160, 735, F3, 41) (dual of [735, 575, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(39) [i] based on
- linear OA(3160, 729, F3, 41) (dual of [729, 569, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3154, 729, F3, 40) (dual of [729, 575, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 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(3169, 838, F3, 2, 41) (dual of [(838, 2), 1507, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3169, 838, F3, 3, 41) (dual of [(838, 3), 2345, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3169, 838, F3, 4, 41) (dual of [(838, 4), 3183, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3169, 838, F3, 5, 41) (dual of [(838, 5), 4021, 42]-NRT-code) | [i] | ||
| 5 | Digital (128, 169, 838)-net over F3 | [i] | ||
| 6 | Linear OOA(3169, 419, F3, 2, 41) (dual of [(419, 2), 669, 42]-NRT-code) | [i] | OOA Folding | |