Information on Result #1196246
Digital (63, 75, 1400713)-net over F25, using net defined by OOA based on linear OOA(2575, 1400713, F25, 14, 12) (dual of [(1400713, 14), 19609907, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2575, 4202140, F25, 2, 12) (dual of [(4202140, 2), 8404205, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2575, 4202141, F25, 2, 12) (dual of [(4202141, 2), 8404207, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2519, 7840, F25, 2, 6) (dual of [(7840, 2), 15661, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(253, 26, F25, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;49,25) [i]
- linear OOA(2516, 7814, F25, 2, 6) (dual of [(7814, 2), 15612, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2516, 15628, F25, 6) (dual of [15628, 15612, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2516, 15625, F25, 6) (dual of [15625, 15609, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2513, 15625, F25, 5) (dual of [15625, 15612, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 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
- OOA 2-folding [i] based on linear OA(2516, 15628, F25, 6) (dual of [15628, 15612, 7]-code), using
- linear OOA(253, 26, F25, 2, 3) (dual of [(26, 2), 49, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2556, 4194301, F25, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- linear OOA(2519, 7840, F25, 2, 6) (dual of [(7840, 2), 15661, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2575, 4202141, F25, 2, 12) (dual of [(4202141, 2), 8404207, 13]-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 (138, 150, 2801426)-net over F5 | [i] | Trace Code for Nets | |