Information on Result #1802050
Digital (67, 84, 1048610)-net over F16, using embedding of OOA with Gilbert–Varšamov bound 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
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.