Information on Result #1195996
Digital (42, 50, 2194808)-net over F25, using net defined by OOA based on linear OOA(2550, 2194808, F25, 10, 8) (dual of [(2194808, 10), 21948030, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2550, 4389617, F25, 2, 8) (dual of [(4389617, 2), 8779184, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2550, 4389618, F25, 2, 8) (dual of [(4389618, 2), 8779186, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2514, 195317, F25, 2, 4) (dual of [(195317, 2), 390620, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2514, 390634, F25, 4) (dual of [390634, 390620, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(255, 390625, F25, 2) (dual of [390625, 390620, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OOA 2-folding [i] based on linear OA(2514, 390634, F25, 4) (dual of [390634, 390620, 5]-code), using
- linear OOA(2536, 4194301, F25, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- linear OOA(2514, 195317, F25, 2, 4) (dual of [(195317, 2), 390620, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2550, 4389618, F25, 2, 8) (dual of [(4389618, 2), 8779186, 9]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (92, 100, 4389616)-net over F5 | [i] | Trace Code for Nets | |