Information on Result #713893
Linear OA(7110, 394, F7, 36) (dual of [394, 284, 37]-code), using construction XX applied to C1 = C([41,71]), C2 = C([36,62]), C3 = C1 + C2 = C([41,62]), and C∩ = C1 ∩ C2 = C([36,71]) based on
- linear OA(779, 342, F7, 31) (dual of [342, 263, 32]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {41,42,…,71}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(770, 342, F7, 27) (dual of [342, 272, 28]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {36,37,…,62}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(791, 342, F7, 36) (dual of [342, 251, 37]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {36,37,…,71}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(758, 342, F7, 22) (dual of [342, 284, 23]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {41,42,…,62}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(713, 34, F7, 8) (dual of [34, 21, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(713, 48, F7, 8) (dual of [48, 35, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(713, 48, F7, 8) (dual of [48, 35, 9]-code), using
- linear OA(76, 18, F7, 4) (dual of [18, 12, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), 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(7110, 197, F7, 2, 36) (dual of [(197, 2), 284, 37]-NRT-code) | [i] | OOA Folding | |