Information on Result #1789754
Digital (37, 45, 786058)-net over F7, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(745, 786058, F7, 8) (dual of [786058, 786013, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(745, 823553, F7, 8) (dual of [823553, 823508, 9]-code), using
- 1 times code embedding in larger space [i] based on linear OA(744, 823552, F7, 8) (dual of [823552, 823508, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- 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(736, 823543, F7, 6) (dual of [823543, 823507, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(78, 9, F7, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,7)), using
- dual of repetition code with length 9 [i]
- linear OA(71, 9, F7, 1) (dual of [9, 8, 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(7) ⊂ Ce(5) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(744, 823552, F7, 8) (dual of [823552, 823508, 9]-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.