Information on Result #814859
Linear OOA(3155, 3286, F3, 2, 29) (dual of [(3286, 2), 6417, 30]-NRT-code), using OOA 2-folding based on linear OA(3155, 6572, F3, 29) (dual of [6572, 6417, 30]-code), using
- construction XX applied to Ce(28) ⊂ Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3153, 6561, F3, 29) (dual of [6561, 6408, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(3155, 3286, F3, 3, 29) (dual of [(3286, 3), 9703, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3155, 3286, F3, 4, 29) (dual of [(3286, 4), 12989, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3155, 3286, F3, 5, 29) (dual of [(3286, 5), 16275, 30]-NRT-code) | [i] | ||
| 4 | Digital (126, 155, 3286)-net over F3 | [i] | ||