Information on Result #814440
Linear OOA(3142, 3291, F3, 2, 26) (dual of [(3291, 2), 6440, 27]-NRT-code), using OOA 2-folding based on linear OA(3142, 6582, F3, 26) (dual of [6582, 6440, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3142, 6583, F3, 26) (dual of [6583, 6441, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(22) ⊂ Ce(21) [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(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(34, 21, F3, 2) (dual of [21, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(25) ⊂ Ce(22) ⊂ 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(3142, 3291, F3, 3, 26) (dual of [(3291, 3), 9731, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3142, 3291, F3, 4, 26) (dual of [(3291, 4), 13022, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3142, 3291, F3, 5, 26) (dual of [(3291, 5), 16313, 27]-NRT-code) | [i] | ||
| 4 | Digital (116, 142, 3291)-net over F3 | [i] | ||