Information on Result #814752
Linear OOA(3198, 29558, F3, 2, 28) (dual of [(29558, 2), 58918, 29]-NRT-code), using OOA 2-folding based on linear OA(3198, 59116, F3, 28) (dual of [59116, 58918, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [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(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(317, 67, F3, 7) (dual of [67, 50, 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(3198, 27980, F3, 3, 28) (dual of [(27980, 3), 83742, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3198, 27980, F3, 4, 28) (dual of [(27980, 4), 111722, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3198, 27980, F3, 5, 28) (dual of [(27980, 5), 139702, 29]-NRT-code) | [i] | ||
| 4 | Digital (170, 198, 27980)-net over F3 | [i] | ||