Information on Result #713382
Linear OA(747, 358, F7, 17) (dual of [358, 311, 18]-code), using construction XX applied to C1 = C([42,57]), C2 = C([46,58]), C3 = C1 + C2 = C([46,57]), and C∩ = C1 ∩ C2 = C([42,58]) 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 = {42,43,…,57}, and designed minimum distance d ≥ |I|+1 = 17 [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(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(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 = {46,47,…,57}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(74, 13, F7, 3) (dual of [13, 9, 4]-code or 13-cap in PG(3,7)), using
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OOA(747, 179, F7, 2, 17) (dual of [(179, 2), 311, 18]-NRT-code) | [i] | OOA Folding | |