Information on Result #713360
Linear OA(754, 371, F7, 18) (dual of [371, 317, 19]-code), using construction XX applied to C1 = C([49,64]), C2 = C([47,58]), C3 = C1 + C2 = C([49,58]), and C∩ = C1 ∩ C2 = C([47,64]) based on
- linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {49,50,…,64}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(731, 342, F7, 12) (dual of [342, 311, 13]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {47,48,…,58}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(746, 342, F7, 18) (dual of [342, 296, 19]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {47,48,…,64}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {49,50,…,58}, and designed minimum distance d ≥ |I|+1 = 11 [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(755, 372, F7, 18) (dual of [372, 317, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(754, 185, F7, 2, 18) (dual of [(185, 2), 316, 19]-NRT-code) | [i] | OOA Folding | |