Information on Result #1725216
Digital (65, 77, 411789)-net over F7, using net defined by OOA based on linear OOA(777, 411789, F7, 15, 12) (dual of [(411789, 15), 6176758, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(777, 823579, F7, 3, 12) (dual of [(823579, 3), 2470660, 13]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(777, 823579, F7, 12) (dual of [823579, 823502, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(775, 823575, F7, 12) (dual of [823575, 823500, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(74, 32, F7, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,7)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(775, 823577, F7, 11) (dual of [823577, 823502, 12]-code), using Gilbert–Varšamov bound and bm = 775 > Vbs−1(k−1) = 2 392012 488029 206879 658599 954080 943155 411035 176907 714533 502017 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(775, 823575, F7, 12) (dual of [823575, 823500, 13]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(777, 823579, F7, 12) (dual of [823579, 823502, 13]-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.