Information on Result #675239
Linear OA(3198, 19745, F3, 31) (dual of [19745, 19547, 32]-code), using construction X applied to Ce(30) ⊂ Ce(22) based on
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(317, 62, F3, 7) (dual of [62, 45, 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, 10140, F3, 2, 31) (dual of [(10140, 2), 20082, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3198, 10140, F3, 3, 31) (dual of [(10140, 3), 30222, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3198, 10140, F3, 4, 31) (dual of [(10140, 4), 40362, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3198, 10140, F3, 5, 31) (dual of [(10140, 5), 50502, 32]-NRT-code) | [i] | ||
| 5 | Digital (167, 198, 10140)-net over F3 | [i] | ||
| 6 | Linear OOA(3198, 3949, F3, 5, 31) (dual of [(3949, 5), 19547, 32]-NRT-code) | [i] | OOA Folding | |