Information on Result #713574
Linear OA(772, 371, F7, 25) (dual of [371, 299, 26]-code), using construction XX applied to C1 = C([42,64]), C2 = C([40,58]), C3 = C1 + C2 = C([42,58]), and C∩ = C1 ∩ C2 = C([40,64]) based on
- 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(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 = {40,41,…,58}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(764, 342, F7, 25) (dual of [342, 278, 26]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {40,41,…,64}, and designed minimum distance d ≥ |I|+1 = 26 [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(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(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [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 OA(773, 372, F7, 25) (dual of [372, 299, 26]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(772, 185, F7, 2, 25) (dual of [(185, 2), 298, 26]-NRT-code) | [i] | OOA Folding | |