Information on Result #953733
Linear OOA(3181, 19686, F3, 3, 27) (dual of [(19686, 3), 58877, 28]-NRT-code), using OOA 3-folding based on linear OA(3181, 59058, F3, 27) (dual of [59058, 58877, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, 59059, F3, 27) (dual of [59059, 58878, 28]-code), using
- 1 times truncation [i] based on linear OA(3182, 59060, F3, 28) (dual of [59060, 58878, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 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
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- 1 times truncation [i] based on linear OA(3182, 59060, F3, 28) (dual of [59060, 58878, 29]-code), using
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(3181, 19686, F3, 4, 27) (dual of [(19686, 4), 78563, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3181, 19686, F3, 5, 27) (dual of [(19686, 5), 98249, 28]-NRT-code) | [i] | ||
| 3 | Digital (154, 181, 19686)-net over F3 | [i] | ||