Information on Result #1793898
Digital (99, 117, 2097206)-net over F8, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8117, 2097206, F8, 18) (dual of [2097206, 2097089, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8116, 2097204, F8, 18) (dual of [2097204, 2097088, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(8116, 2097205, F8, 17) (dual of [2097205, 2097089, 18]-code), using Gilbert–Varšamov bound and bm = 8116 > Vbs−1(k−1) = 222420 855975 125301 125171 722968 421660 507470 942101 409441 101012 939545 927363 596226 634562 660654 648257 896231 [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(8116, 2097204, F8, 18) (dual of [2097204, 2097088, 19]-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.