Information on Result #1221178
Digital (69, 82, 1528309)-net over F25, using (u, u+v)-construction based on
- digital (15, 21, 130209)-net over F25, using
- net defined by OOA [i] based on linear OOA(2521, 130209, F25, 6, 6) (dual of [(130209, 6), 781233, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2521, 390627, F25, 6) (dual of [390627, 390606, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(2521, 390629, F25, 6) (dual of [390629, 390608, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2521, 390625, F25, 6) (dual of [390625, 390604, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2517, 390625, F25, 5) (dual of [390625, 390608, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2521, 390629, F25, 6) (dual of [390629, 390608, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(2521, 390627, F25, 6) (dual of [390627, 390606, 7]-code), using
- net defined by OOA [i] based on linear OOA(2521, 130209, F25, 6, 6) (dual of [(130209, 6), 781233, 7]-NRT-code), using
- digital (48, 61, 1398100)-net over F25, using
- net defined by OOA [i] based on linear OOA(2561, 1398100, F25, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2561, 8388601, F25, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2561, 8388601, F25, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(2561, 1398100, F25, 13, 13) (dual of [(1398100, 13), 18175239, 14]-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 (95, 108, 3056618)-net over F25 | [i] | (u, u+v)-Construction for Nets | |