Information on Result #1813475
Digital (18, 36, 4406)-net over F128, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12836, 4406, F128, 3, 18) (dual of [(4406, 3), 13182, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12836, 5463, F128, 3, 18) (dual of [(5463, 3), 16353, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12836, 16389, F128, 18) (dual of [16389, 16353, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- OOA 3-folding [i] based on linear OA(12836, 16389, F128, 18) (dual of [16389, 16353, 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | (24, 42, 4406)-net in base 64 | [i] | Base Change | |