Information on Result #813685
Linear OOA(3124, 9858, F3, 2, 20) (dual of [(9858, 2), 19592, 21]-NRT-code), using OOA 2-folding based on linear OA(3124, 19716, F3, 20) (dual of [19716, 19592, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-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
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(3126, 9859, F3, 2, 20) (dual of [(9859, 2), 19592, 21]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3125, 9858, F3, 2, 20) (dual of [(9858, 2), 19591, 21]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3124, 9511, F3, 3, 20) (dual of [(9511, 3), 28409, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3124, 9511, F3, 4, 20) (dual of [(9511, 4), 37920, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(3124, 9511, F3, 5, 20) (dual of [(9511, 5), 47431, 21]-NRT-code) | [i] | ||
| 6 | Digital (104, 124, 9511)-net over F3 | [i] | ||