Information on Result #1794218
Digital (105, 124, 2097206)-net over F8, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8124, 2097206, F8, 19) (dual of [2097206, 2097082, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8123, 2097204, F8, 19) (dual of [2097204, 2097081, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(18) ⊂ Ce(11) [i] based on
- linear OA(8123, 2097205, F8, 18) (dual of [2097205, 2097082, 19]-code), using Gilbert–Varšamov bound and bm = 8123 > Vbs−1(k−1) = 192071 098419 301344 636990 325070 177497 771086 327882 579491 721067 134389 235851 727664 358288 841664 542354 344430 931291 [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(8123, 2097204, F8, 19) (dual of [2097204, 2097081, 20]-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.