Information on Result #1790172
Digital (57, 67, 5764821)-net over F7, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(767, 5764821, F7, 10) (dual of [5764821, 5764754, 11]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(766, 5764819, F7, 10) (dual of [5764819, 5764753, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(717, 18, F7, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,7)), using
- dual of repetition code with length 18 [i]
- linear OA(71, 18, F7, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(766, 5764820, F7, 9) (dual of [5764820, 5764754, 10]-code), using Gilbert–Varšamov bound and bm = 766 > Vbs−1(k−1) = 50 812771 086022 967893 912537 396962 810040 553914 071512 474071 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 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(766, 5764819, F7, 10) (dual of [5764819, 5764753, 11]-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.