Information on Result #2678061
Linear OOA(3209, 59063, F3, 3, 28) (dual of [(59063, 3), 176980, 29]-NRT-code), using 31 times duplication based on linear OOA(3208, 59063, F3, 3, 28) (dual of [(59063, 3), 176981, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3208, 177189, F3, 28) (dual of [177189, 176981, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3207, 177188, F3, 28) (dual of [177188, 176981, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3207, 177188, F3, 28) (dual of [177188, 176981, 29]-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(3209, 59063, F3, 4, 28) (dual of [(59063, 4), 236043, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3209, 59063, F3, 5, 28) (dual of [(59063, 5), 295106, 29]-NRT-code) | [i] | ||
| 3 | Digital (181, 209, 59063)-net over F3 | [i] | ||