Information on Result #814436
Linear OOA(3138, 3285, F3, 2, 26) (dual of [(3285, 2), 6432, 27]-NRT-code), using OOA 2-folding based on linear OA(3138, 6570, F3, 26) (dual of [6570, 6432, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3137, 6569, F3, 26) (dual of [6569, 6432, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [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(3138, 3102, F3, 3, 26) (dual of [(3102, 3), 9168, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3138, 3102, F3, 4, 26) (dual of [(3102, 4), 12270, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3138, 3102, F3, 5, 26) (dual of [(3102, 5), 15372, 27]-NRT-code) | [i] | ||
| 4 | Digital (112, 138, 3102)-net over F3 | [i] | ||