Information on Result #815289
Linear OOA(3218, 29543, F3, 2, 32) (dual of [(29543, 2), 58868, 33]-NRT-code), using OOA 2-folding based on linear OA(3218, 59086, F3, 32) (dual of [59086, 58868, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3217, 59085, F3, 32) (dual of [59085, 58868, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(3211, 59049, F3, 32) (dual of [59049, 58838, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- 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(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(31) ⊂ Ce(27) [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(3220, 29544, F3, 2, 32) (dual of [(29544, 2), 58868, 33]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3219, 29543, F3, 2, 32) (dual of [(29543, 2), 58867, 33]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3218, 20856, F3, 3, 32) (dual of [(20856, 3), 62350, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3218, 20856, F3, 4, 32) (dual of [(20856, 4), 83206, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(3218, 20856, F3, 5, 32) (dual of [(20856, 5), 104062, 33]-NRT-code) | [i] | ||
| 6 | Digital (186, 218, 20856)-net over F3 | [i] | ||