Information on Result #814721
Linear OOA(3147, 3286, F3, 2, 28) (dual of [(3286, 2), 6425, 29]-NRT-code), using OOA 2-folding based on linear OA(3147, 6572, F3, 28) (dual of [6572, 6425, 29]-code), using
- construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- 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(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3147, 2954, F3, 3, 28) (dual of [(2954, 3), 8715, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3147, 2954, F3, 4, 28) (dual of [(2954, 4), 11669, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3147, 2954, F3, 5, 28) (dual of [(2954, 5), 14623, 29]-NRT-code) | [i] | ||
| 4 | Digital (119, 147, 2954)-net over F3 | [i] | ||