Information on Result #713621
Linear OA(784, 387, F7, 27) (dual of [387, 303, 28]-code), using construction XX applied to C1 = C([337,15]), C2 = C([1,21]), C3 = C1 + C2 = C([1,15]), and C∩ = C1 ∩ C2 = C([337,21]) based on
- linear OA(755, 342, F7, 21) (dual of [342, 287, 22]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−5,−4,…,15}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(754, 342, F7, 21) (dual of [342, 288, 22]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(770, 342, F7, 27) (dual of [342, 272, 28]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−5,−4,…,21}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(739, 342, F7, 15) (dual of [342, 303, 16]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(77, 23, F7, 5) (dual of [23, 16, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- linear OA(77, 22, F7, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code) (see above)
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 OA(785, 388, F7, 27) (dual of [388, 303, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(784, 193, F7, 2, 27) (dual of [(193, 2), 302, 28]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(784, 129, F7, 3, 27) (dual of [(129, 3), 303, 28]-NRT-code) | [i] | ||