Information on Result #1190006
Digital (69, 78, 2883577)-net over F7, using net defined by OOA based on linear OOA(778, 2883577, F7, 10, 9) (dual of [(2883577, 10), 28835692, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(778, 5767155, F7, 2, 9) (dual of [(5767155, 2), 11534232, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(778, 5767156, F7, 2, 9) (dual of [(5767156, 2), 11534234, 10]-NRT-code), using
- trace code [i] based on linear OOA(4939, 2883578, F49, 2, 9) (dual of [(2883578, 2), 5767117, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4939, 5767156, F49, 9) (dual of [5767156, 5767117, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(4939, 5767157, F49, 9) (dual of [5767157, 5767118, 10]-code), using
- (u, u+v)-construction [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
- 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
- linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4939, 5767157, F49, 9) (dual of [5767157, 5767118, 10]-code), using
- OOA 2-folding [i] based on linear OA(4939, 5767156, F49, 9) (dual of [5767156, 5767117, 10]-code), using
- trace code [i] based on linear OOA(4939, 2883578, F49, 2, 9) (dual of [(2883578, 2), 5767117, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(778, 5767156, F7, 2, 9) (dual of [(5767156, 2), 11534234, 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.