Information on Result #1779269
Digital (158, 192, 16443)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4192, 16443, F4, 34) (dual of [16443, 16251, 35]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4190, 16440, F4, 34) (dual of [16440, 16250, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(33) ⊂ Ce(25) [i] based on
- linear OA(4190, 16441, F4, 32) (dual of [16441, 16251, 33]-code), using Gilbert–Varšamov bound and bm = 4190 > Vbs−1(k−1) = 3603 092496 508275 938237 839199 608426 398294 719346 727132 500788 600047 218404 713769 295256 698755 178995 345763 906858 872524 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4190, 16440, F4, 34) (dual of [16440, 16250, 35]-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.