Information on Result #713514
Linear OA(769, 377, F7, 23) (dual of [377, 308, 24]-code), using construction XX applied to C1 = C([46,64]), C2 = C([42,58]), C3 = C1 + C2 = C([46,58]), and C∩ = C1 ∩ C2 = C([42,64]) based on
- linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {46,47,…,64}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {42,43,…,58}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(758, 342, F7, 23) (dual of [342, 284, 24]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {42,43,…,64}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(734, 342, F7, 13) (dual of [342, 308, 14]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {46,47,…,58}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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), using
- linear OA(74, 13, F7, 3) (dual of [13, 9, 4]-code or 13-cap in PG(3,7)), using
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(770, 378, F7, 23) (dual of [378, 308, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(769, 188, F7, 2, 23) (dual of [(188, 2), 307, 24]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(769, 125, F7, 3, 23) (dual of [(125, 3), 306, 24]-NRT-code) | [i] | ||