Information on Result #1734495
Linear OOA(1684, 262152, F16, 18, 17) (dual of [(262152, 18), 4718652, 18]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OOA(1684, 1048609, F16, 2, 17) (dual of [(1048609, 2), 2097134, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1684, 1048610, F16, 2, 17) (dual of [(1048610, 2), 2097136, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1684, 1048610, F16, 17) (dual of [1048610, 1048526, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1683, 1048608, F16, 17) (dual of [1048608, 1048525, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1651, 1048576, F16, 11) (dual of [1048576, 1048525, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(167, 32, F16, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(1683, 1048609, F16, 16) (dual of [1048609, 1048526, 17]-code), using Gilbert–Varšamov bound and bm = 1683 > Vbs−1(k−1) = 682375 934352 272467 710614 302455 931600 613801 454964 372929 533539 633528 191006 338985 131069 790872 499421 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(1683, 1048608, F16, 17) (dual of [1048608, 1048525, 18]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1684, 1048610, F16, 17) (dual of [1048610, 1048526, 18]-code), using
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (67, 84, 262152)-net over F16 | [i] | Net Defined by OOA | |