Information on Result #1190004
Digital (68, 77, 2882989)-net over F7, using net defined by OOA based on linear OOA(777, 2882989, F7, 10, 9) (dual of [(2882989, 10), 28829813, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(777, 5765979, F7, 2, 9) (dual of [(5765979, 2), 11531881, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(777, 5765980, F7, 2, 9) (dual of [(5765980, 2), 11531883, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(711, 1176, F7, 2, 4) (dual of [(1176, 2), 2341, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(711, 2352, F7, 4) (dual of [2352, 2341, 5]-code), using
- base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- 1 times truncation [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- OOA 2-folding [i] based on linear OA(711, 2352, F7, 4) (dual of [2352, 2341, 5]-code), using
- linear OOA(766, 5764804, F7, 2, 9) (dual of [(5764804, 2), 11529542, 10]-NRT-code), using
- trace code [i] based on linear OOA(4933, 2882402, F49, 2, 9) (dual of [(2882402, 2), 5764771, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4933, 5764804, F49, 9) (dual of [5764804, 5764771, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(4933, 5764805, F49, 9) (dual of [5764805, 5764772, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4933, 5764805, F49, 9) (dual of [5764805, 5764772, 10]-code), using
- OOA 2-folding [i] based on linear OA(4933, 5764804, F49, 9) (dual of [5764804, 5764771, 10]-code), using
- trace code [i] based on linear OOA(4933, 2882402, F49, 2, 9) (dual of [(2882402, 2), 5764771, 10]-NRT-code), using
- linear OOA(711, 1176, F7, 2, 4) (dual of [(1176, 2), 2341, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(777, 5765980, F7, 2, 9) (dual of [(5765980, 2), 11531883, 10]-NRT-code), using
Mode: Constructive and 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.