Information on Result #815409
Linear OOA(3226, 29538, F3, 2, 33) (dual of [(29538, 2), 58850, 34]-NRT-code), using OOA 2-folding based on linear OA(3226, 59076, F3, 33) (dual of [59076, 58850, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3226, 59077, F3, 33) (dual of [59077, 58851, 34]-code), using
- construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3191, 59049, F3, 29) (dual of [59049, 58858, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 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(33) ⊂ Ce(30) ⊂ Ce(28) [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(3226, 21963, F3, 3, 33) (dual of [(21963, 3), 65663, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3226, 21963, F3, 4, 33) (dual of [(21963, 4), 87626, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3226, 21963, F3, 5, 33) (dual of [(21963, 5), 109589, 34]-NRT-code) | [i] | ||
| 4 | Digital (193, 226, 21963)-net over F3 | [i] | ||