Information on Result #1302412
Linear OA(843, 8198, F8, 11) (dual of [8198, 8155, 12]-code), using construction X with Varšamov bound based on
- linear OA(842, 8196, F8, 11) (dual of [8196, 8154, 12]-code), using
- trace code [i] based on linear OA(6421, 4098, F64, 11) (dual of [4098, 4077, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(6421, 4096, F64, 11) (dual of [4096, 4075, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- trace code [i] based on linear OA(6421, 4098, F64, 11) (dual of [4098, 4077, 12]-code), using
- linear OA(842, 8197, F8, 10) (dual of [8197, 8155, 11]-code), using Gilbert–Varšamov bound and bm = 842 > Vbs−1(k−1) = 18 479781 192533 737122 457795 483129 121792 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(843, 8198, F8, 2, 11) (dual of [(8198, 2), 16353, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(843, 8198, F8, 3, 11) (dual of [(8198, 3), 24551, 12]-NRT-code) | [i] | ||
| 3 | Digital (32, 43, 8198)-net over F8 | [i] | ||
| 4 | Linear OOA(843, 4099, F8, 2, 11) (dual of [(4099, 2), 8155, 12]-NRT-code) | [i] | OOA Folding | |