Information on Result #813364
Linear OOA(3118, 29543, F3, 2, 17) (dual of [(29543, 2), 58968, 18]-NRT-code), using OOA 2-folding based on linear OA(3118, 59086, F3, 17) (dual of [59086, 58968, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(381, 59049, F3, 13) (dual of [59049, 58968, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
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(3120, 29544, F3, 2, 17) (dual of [(29544, 2), 58968, 18]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3119, 29543, F3, 2, 17) (dual of [(29543, 2), 58967, 18]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3118, 27134, F3, 3, 17) (dual of [(27134, 3), 81284, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3118, 27134, F3, 4, 17) (dual of [(27134, 4), 108418, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(3118, 27134, F3, 5, 17) (dual of [(27134, 5), 135552, 18]-NRT-code) | [i] | ||
| 6 | Digital (101, 118, 27134)-net over F3 | [i] | ||