Information on Result #815022
Linear OOA(3218, 29563, F3, 2, 30) (dual of [(29563, 2), 58908, 31]-NRT-code), using OOA 2-folding based on linear OA(3218, 59126, F3, 30) (dual of [59126, 58908, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(21) [i] based on
- 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(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(317, 77, F3, 7) (dual of [77, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(317, 80, F3, 7) (dual of [80, 63, 8]-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(3219, 29563, F3, 2, 30) (dual of [(29563, 2), 58907, 31]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3218, 29563, F3, 3, 30) (dual of [(29563, 3), 88471, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3218, 29563, F3, 4, 30) (dual of [(29563, 4), 118034, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3218, 29563, F3, 5, 30) (dual of [(29563, 5), 147597, 31]-NRT-code) | [i] | ||
| 5 | Digital (188, 218, 29563)-net over F3 | [i] | ||