Information on Result #676186
Linear OA(3178, 2218, F3, 37) (dual of [2218, 2040, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(31) ⊂ Ce(30) based on
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3141, 2187, F3, 31) (dual of [2187, 2046, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(3178, 1767, F3, 2, 37) (dual of [(1767, 2), 3356, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3178, 1767, F3, 3, 37) (dual of [(1767, 3), 5123, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3178, 1767, F3, 4, 37) (dual of [(1767, 4), 6890, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3178, 1767, F3, 5, 37) (dual of [(1767, 5), 8657, 38]-NRT-code) | [i] | ||
| 5 | Digital (141, 178, 1767)-net over F3 | [i] | ||
| 6 | Linear OOA(3178, 1109, F3, 2, 37) (dual of [(1109, 2), 2040, 38]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3178, 739, F3, 3, 37) (dual of [(739, 3), 2039, 38]-NRT-code) | [i] | ||