Information on Result #1189834
Digital (56, 63, 7686403)-net over F7, using net defined by OOA based on linear OOA(763, 7686403, F7, 9, 7) (dual of [(7686403, 9), 69177564, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(763, 7686404, F7, 3, 7) (dual of [(7686404, 3), 23059149, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(713, 6120101, F7, 3, 3) (dual of [(6120101, 3), 18360290, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(713, 6120101, F7, 2, 3) (dual of [(6120101, 2), 12240189, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(713, 6120101, F7, 3) (dual of [6120101, 6120088, 4]-code or 6120101-cap in PG(12,7)), using
- appending kth column [i] based on linear OOA(713, 6120101, F7, 2, 3) (dual of [(6120101, 2), 12240189, 4]-NRT-code), using
- linear OOA(750, 3843202, F7, 3, 7) (dual of [(3843202, 3), 11529556, 8]-NRT-code), using
- trace code [i] based on linear OOA(4925, 1921601, F49, 3, 7) (dual of [(1921601, 3), 5764778, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4925, 5764803, F49, 7) (dual of [5764803, 5764778, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- OOA 3-folding [i] based on linear OA(4925, 5764803, F49, 7) (dual of [5764803, 5764778, 8]-code), using
- trace code [i] based on linear OOA(4925, 1921601, F49, 3, 7) (dual of [(1921601, 3), 5764778, 8]-NRT-code), using
- linear OOA(713, 6120101, F7, 3, 3) (dual of [(6120101, 3), 18360290, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
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.