Information on Result #1792705
Digital (69, 83, 524304)-net over F8, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(883, 524304, F8, 14) (dual of [524304, 524221, 15]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(882, 524302, F8, 14) (dual of [524302, 524220, 15]-code), using
- trace code [i] based on linear OA(6441, 262151, F64, 14) (dual of [262151, 262110, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- trace code [i] based on linear OA(6441, 262151, F64, 14) (dual of [262151, 262110, 15]-code), using
- linear OA(882, 524303, F8, 13) (dual of [524303, 524221, 14]-code), using Gilbert–Varšamov bound and bm = 882 > Vbs−1(k−1) = 12467 071163 921913 335205 861863 299549 766260 685392 859729 835010 695915 934989 [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(882, 524302, F8, 14) (dual of [524302, 524220, 15]-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.