Information on Result #676213
Linear OA(3136, 2218, F3, 28) (dual of [2218, 2082, 29]-code), using construction XX applied to Ce(27) ⊂ Ce(22) ⊂ Ce(21) based on
- linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3106, 2187, F3, 23) (dual of [2187, 2081, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(399, 2187, F3, 22) (dual of [2187, 2088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(38, 30, F3, 4) (dual of [30, 22, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3136, 1559, F3, 2, 28) (dual of [(1559, 2), 2982, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3136, 1559, F3, 3, 28) (dual of [(1559, 3), 4541, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3136, 1559, F3, 4, 28) (dual of [(1559, 4), 6100, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3136, 1559, F3, 5, 28) (dual of [(1559, 5), 7659, 29]-NRT-code) | [i] | ||
| 5 | Digital (108, 136, 1559)-net over F3 | [i] | ||
| 6 | Linear OOA(3136, 1109, F3, 2, 28) (dual of [(1109, 2), 2082, 29]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3136, 739, F3, 3, 28) (dual of [(739, 3), 2081, 29]-NRT-code) | [i] | ||