Information on Result #1792286
Digital (49, 65, 8204)-net over F8, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(865, 8204, F8, 16) (dual of [8204, 8139, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(864, 8202, F8, 16) (dual of [8202, 8138, 17]-code), using
- trace code [i] based on linear OA(6432, 4101, F64, 16) (dual of [4101, 4069, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- trace code [i] based on linear OA(6432, 4101, F64, 16) (dual of [4101, 4069, 17]-code), using
- linear OA(864, 8203, F8, 15) (dual of [8203, 8139, 16]-code), using Gilbert–Varšamov bound and bm = 864 > Vbs−1(k−1) = 47 987255 931712 017602 293002 712709 224088 638783 405907 595264 [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(864, 8202, F8, 16) (dual of [8202, 8138, 17]-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.