Information on Result #1746816
Digital (10, 17, 32770)-net over F128, using net defined by OOA based on linear OOA(12817, 32770, F128, 9, 7) (dual of [(32770, 9), 294913, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(12817, 32771, F128, 3, 7) (dual of [(32771, 3), 98296, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12817, 32771, F128, 7) (dual of [32771, 32754, 8]-code), using
- (u, u+v)-construction [i] based on
- linear OA(1284, 16385, F128, 3) (dual of [16385, 16381, 4]-code or 16385-cap in PG(3,128)), using
- linear OA(12813, 16386, F128, 7) (dual of [16386, 16373, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(12813, 16384, F128, 7) (dual of [16384, 16371, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12817, 32771, F128, 7) (dual of [32771, 32754, 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.