Information on Result #1726842
Digital (20, 27, 8197)-net over F8, using net defined by OOA based on linear OOA(827, 8197, F8, 9, 7) (dual of [(8197, 9), 73746, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(827, 8198, F8, 3, 7) (dual of [(8198, 3), 24567, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(827, 8198, F8, 7) (dual of [8198, 8171, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(826, 8196, F8, 7) (dual of [8196, 8170, 8]-code), using
- trace code [i] based on linear OA(6413, 4098, F64, 7) (dual of [4098, 4085, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6413, 4098, F64, 7) (dual of [4098, 4085, 8]-code), using
- linear OA(826, 8197, F8, 6) (dual of [8197, 8171, 7]-code), using Gilbert–Varšamov bound and bm = 826 > Vbs−1(k−1) = 5174 001952 051112 933376 [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
- linear OA(826, 8196, F8, 7) (dual of [8196, 8170, 8]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(827, 8198, F8, 7) (dual of [8198, 8171, 8]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.