Information on Result #1441476
Linear OOA(768, 823569, F7, 2, 11) (dual of [(823569, 2), 1647070, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(768, 823569, F7, 11) (dual of [823569, 823501, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(767, 823567, F7, 11) (dual of [823567, 823500, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(73, 24, F7, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(767, 823568, F7, 10) (dual of [823568, 823501, 11]-code), using Gilbert–Varšamov bound and bm = 767 > Vbs−1(k−1) = 4 840279 651358 749106 281326 410063 030570 619290 090378 459191 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 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
- linear OA(767, 823567, F7, 11) (dual of [823567, 823500, 12]-code), using
Mode: 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(768, 411784, F7, 3, 11) (dual of [(411784, 3), 1235284, 12]-NRT-code) | [i] | OOA Folding | |