Information on Result #1780537
Digital (171, 208, 16447)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4208, 16447, F4, 37) (dual of [16447, 16239, 38]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4204, 16440, F4, 37) (dual of [16440, 16236, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(36) ⊂ Ce(28) [i] based on
- linear OA(4204, 16443, F4, 35) (dual of [16443, 16239, 36]-code), using Gilbert–Varšamov bound and bm = 4204 > Vbs−1(k−1) = 12 019539 494527 898140 633992 342083 572364 819766 679581 739340 328200 830035 120618 111899 539454 827818 927825 806185 000388 754046 660564 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 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(4204, 16440, F4, 37) (dual of [16440, 16236, 38]-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.