Information on Result #1220986
Digital (51, 61, 1685869)-net over F25, using (u, u+v)-construction based on
- digital (10, 15, 8149)-net over F25, using
- net defined by OOA [i] based on linear OOA(2515, 8149, F25, 6, 5) (dual of [(8149, 6), 48879, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2515, 8150, F25, 2, 5) (dual of [(8150, 2), 16285, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(250, s, F25, 2, 0) for arbitrarily large s, using
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code) (see above)
- linear OOA(251, 326, F25, 2, 1) (dual of [(326, 2), 651, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(251, s, F25, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(251, s, F25, 2, 1) for arbitrarily large s, using
- linear OOA(251, 326, F25, 2, 1) (dual of [(326, 2), 651, 2]-NRT-code) (see above)
- linear OOA(251, 326, F25, 2, 1) (dual of [(326, 2), 651, 2]-NRT-code) (see above)
- linear OOA(253, 326, F25, 2, 2) (dual of [(326, 2), 649, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(253, 651, F25, 2, 2) (dual of [(651, 2), 1299, 3]-NRT-code), using
- appending kth column [i] based on linear OA(253, 651, F25, 2) (dual of [651, 648, 3]-code), using
- Hamming code H(3,25) [i]
- appending kth column [i] based on linear OA(253, 651, F25, 2) (dual of [651, 648, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(253, 651, F25, 2, 2) (dual of [(651, 2), 1299, 3]-NRT-code), using
- linear OOA(259, 326, F25, 2, 5) (dual of [(326, 2), 643, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(252, 26, F25, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;50,25) [i]
- linear OOA(257, 300, F25, 2, 5) (dual of [(300, 2), 593, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(257, 600, F25, 5) (dual of [600, 593, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- OOA 2-folding [i] based on linear OA(257, 600, F25, 5) (dual of [600, 593, 6]-code), using
- linear OOA(252, 26, F25, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(250, 326, F25, 2, 0) (dual of [(326, 2), 652, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(2515, 8150, F25, 2, 5) (dual of [(8150, 2), 16285, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2515, 8149, F25, 6, 5) (dual of [(8149, 6), 48879, 6]-NRT-code), using
- digital (36, 46, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-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 (72, 82, 3371738)-net over F25 | [i] | (u, u+v)-Construction for Nets | |