Information on Result #675633
Linear OA(3222, 6583, F3, 41) (dual of [6583, 6361, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(37) ⊂ Ce(36) based on
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(3222, 3854, F3, 2, 41) (dual of [(3854, 2), 7486, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3222, 3854, F3, 3, 41) (dual of [(3854, 3), 11340, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3222, 3854, F3, 4, 41) (dual of [(3854, 4), 15194, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3222, 3854, F3, 5, 41) (dual of [(3854, 5), 19048, 42]-NRT-code) | [i] | ||
| 5 | Digital (181, 222, 3854)-net over F3 | [i] | ||
| 6 | Linear OOA(3222, 3291, F3, 2, 41) (dual of [(3291, 2), 6360, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3222, 2194, F3, 3, 41) (dual of [(2194, 3), 6360, 42]-NRT-code) | [i] | ||