Information on Result #675663
Linear OA(3174, 6583, F3, 32) (dual of [6583, 6409, 33]-code), using construction XX applied to Ce(31) ⊂ Ce(28) ⊂ Ce(27) based on
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3153, 6561, F3, 29) (dual of [6561, 6408, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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]
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(3174, 3369, F3, 2, 32) (dual of [(3369, 2), 6564, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3174, 3369, F3, 3, 32) (dual of [(3369, 3), 9933, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3174, 3369, F3, 4, 32) (dual of [(3369, 4), 13302, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3174, 3369, F3, 5, 32) (dual of [(3369, 5), 16671, 33]-NRT-code) | [i] | ||
| 5 | Digital (142, 174, 3369)-net over F3 | [i] | ||
| 6 | Linear OOA(3174, 3291, F3, 2, 32) (dual of [(3291, 2), 6408, 33]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3174, 2194, F3, 3, 32) (dual of [(2194, 3), 6408, 33]-NRT-code) | [i] | ||