Information on Result #2677268
Linear OOA(3146, 59053, F3, 3, 20) (dual of [(59053, 3), 177013, 21]-NRT-code), using 31 times duplication based on linear OOA(3145, 59053, F3, 3, 20) (dual of [(59053, 3), 177014, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3145, 177159, F3, 20) (dual of [177159, 177014, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3144, 177158, F3, 20) (dual of [177158, 177014, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3144, 177147, F3, 20) (dual of [177147, 177003, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3144, 177158, F3, 20) (dual of [177158, 177014, 21]-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(3146, 59053, F3, 4, 20) (dual of [(59053, 4), 236066, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3146, 59053, F3, 5, 20) (dual of [(59053, 5), 295119, 21]-NRT-code) | [i] | ||
| 3 | Digital (126, 146, 59053)-net over F3 | [i] | ||