Information on Result #814465
Linear OOA(3178, 29543, F3, 2, 26) (dual of [(29543, 2), 58908, 27]-NRT-code), using OOA 2-folding based on linear OA(3178, 59086, F3, 26) (dual of [59086, 58908, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3177, 59085, F3, 26) (dual of [59085, 58908, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [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(3180, 29544, F3, 2, 26) (dual of [(29544, 2), 58908, 27]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3179, 29543, F3, 2, 26) (dual of [(29543, 2), 58907, 27]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3178, 21086, F3, 3, 26) (dual of [(21086, 3), 63080, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3178, 21086, F3, 4, 26) (dual of [(21086, 4), 84166, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(3178, 21086, F3, 5, 26) (dual of [(21086, 5), 105252, 27]-NRT-code) | [i] | ||
| 6 | Digital (152, 178, 21086)-net over F3 | [i] | ||