Information on Result #713329
Linear OA(751, 371, F7, 17) (dual of [371, 320, 18]-code), using construction XX applied to C1 = C([50,64]), C2 = C([48,58]), C3 = C1 + C2 = C([50,58]), and C∩ = C1 ∩ C2 = C([48,64]) based on
- linear OA(737, 342, F7, 15) (dual of [342, 305, 16]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {50,51,…,64}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {48,49,…,58}, and designed minimum distance d ≥ |I|+1 = 12 [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 = {48,49,…,64}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {50,51,…,58}, and designed minimum distance d ≥ |I|+1 = 10 [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(752, 372, F7, 17) (dual of [372, 320, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(751, 185, F7, 2, 17) (dual of [(185, 2), 319, 18]-NRT-code) | [i] | OOA Folding | |