Information on Result #2487192
Linear OOA(3191, 29544, F3, 2, 28) (dual of [(29544, 2), 58897, 29]-NRT-code), using 31 times duplication based on linear OOA(3190, 29544, F3, 2, 28) (dual of [(29544, 2), 58898, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3190, 59088, F3, 28) (dual of [59088, 58898, 29]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3189, 59087, F3, 28) (dual of [59087, 58898, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [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(3151, 59049, F3, 23) (dual of [59049, 58898, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(38, 38, F3, 4) (dual of [38, 30, 5]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3189, 59087, F3, 28) (dual of [59087, 58898, 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(3191, 20565, F3, 3, 28) (dual of [(20565, 3), 61504, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3191, 20565, F3, 4, 28) (dual of [(20565, 4), 82069, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3191, 20565, F3, 5, 28) (dual of [(20565, 5), 102634, 29]-NRT-code) | [i] | ||
| 4 | Digital (163, 191, 20565)-net over F3 | [i] | ||