Information on Result #1789842
Digital (41, 51, 117665)-net over F7, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(751, 117665, F7, 10) (dual of [117665, 117614, 11]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(750, 117663, F7, 10) (dual of [117663, 117613, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(737, 117649, F7, 8) (dual of [117649, 117612, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(713, 14, F7, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,7)), using
- dual of repetition code with length 14 [i]
- linear OA(71, 14, F7, 1) (dual of [14, 13, 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(750, 117664, F7, 9) (dual of [117664, 117614, 10]-code), using Gilbert–Varšamov bound and bm = 750 > Vbs−1(k−1) = 1 530066 788930 745037 032465 850622 055257 307319 [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(750, 117663, F7, 10) (dual of [117663, 117613, 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.