Information on Result #906822
Linear OOA(3241, large, F32, 2, 7), using generalized (u, u+v)-construction based on
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(320, s, F32, 2, 0) for arbitrarily large s, using
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(320, 524290, F32, 2, 0) (dual of [(524290, 2), 1048580, 1]-NRT-code) (see above)
- linear OOA(321, 524290, F32, 2, 1) (dual of [(524290, 2), 1048579, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(321, s, F32, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(321, s, F32, 2, 1) for arbitrarily large s, using
- linear OOA(321, 524290, F32, 2, 1) (dual of [(524290, 2), 1048579, 2]-NRT-code) (see above)
- linear OOA(321, 524290, F32, 2, 1) (dual of [(524290, 2), 1048579, 2]-NRT-code) (see above)
- linear OOA(321, 524290, F32, 2, 1) (dual of [(524290, 2), 1048579, 2]-NRT-code) (see above)
- linear OOA(325, 524290, F32, 2, 2) (dual of [(524290, 2), 1048575, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(325, 1082401, F32, 2, 2) (dual of [(1082401, 2), 2164797, 3]-NRT-code), using
- appending kth column [i] based on linear OA(325, 1082401, F32, 2) (dual of [1082401, 1082396, 3]-code), using
- Hamming code H(5,32) [i]
- appending kth column [i] based on linear OA(325, 1082401, F32, 2) (dual of [1082401, 1082396, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(325, 1082401, F32, 2, 2) (dual of [(1082401, 2), 2164797, 3]-NRT-code), using
- linear OOA(327, 524290, F32, 2, 3) (dual of [(524290, 2), 1048573, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(327, 1050624, F32, 2, 3) (dual of [(1050624, 2), 2101241, 4]-NRT-code), using
- linear OOA(3225, 524290, F32, 2, 7) (dual of [(524290, 2), 1048555, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3225, 1048580, F32, 7) (dual of [1048580, 1048555, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 2-folding [i] based on linear OA(3225, 1048580, F32, 7) (dual of [1048580, 1048555, 8]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3241, large, F32, 2, 6) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3241, large, F32, 2, 5) | [i] | ||
| 3 | Linear OOA(3241, large, F32, 2, 4) | [i] | ||
| 4 | Linear OOA(3241, large, F32, 2, 3) | [i] | ||
| 5 | Linear OOA(3243, large, F32, 2, 7) | [i] | NRT-Code Embedding in Larger Space | |
| 6 | Linear OOA(3245, large, F32, 2, 7) | [i] | ||
| 7 | Linear OOA(3247, large, F32, 2, 7) | [i] | ||
| 8 | Linear OOA(3249, large, F32, 2, 7) | [i] | ||
| 9 | Linear OOA(3251, large, F32, 2, 7) | [i] | ||
| 10 | Linear OOA(3253, large, F32, 2, 7) | [i] | ||
| 11 | Linear OOA(3255, large, F32, 2, 7) | [i] | ||
| 12 | Linear OOA(3257, large, F32, 2, 7) | [i] | ||
| 13 | Linear OOA(3259, large, F32, 2, 7) | [i] | ||
| 14 | Linear OOA(3261, large, F32, 2, 7) | [i] | ||
| 15 | Linear OOA(3263, large, F32, 2, 7) | [i] | ||
| 16 | Linear OOA(3265, large, F32, 2, 7) | [i] | ||
| 17 | Linear OOA(3267, large, F32, 2, 7) | [i] | ||
| 18 | Linear OOA(3269, large, F32, 2, 7) | [i] | ||
| 19 | Linear OOA(3271, large, F32, 2, 7) | [i] | ||
| 20 | Linear OOA(3273, large, F32, 2, 7) | [i] | ||
| 21 | Linear OOA(3275, large, F32, 2, 7) | [i] | ||
| 22 | Linear OOA(3277, large, F32, 2, 7) | [i] | ||
| 23 | Linear OOA(3279, large, F32, 2, 7) | [i] | ||
| 24 | Linear OOA(3281, large, F32, 2, 7) | [i] | ||
| 25 | Linear OOA(3283, large, F32, 2, 7) | [i] | ||
| 26 | Linear OOA(3285, large, F32, 2, 7) | [i] | ||
| 27 | Linear OOA(3287, large, F32, 2, 7) | [i] | ||
| 28 | Linear OOA(3289, large, F32, 2, 7) | [i] | ||
| 29 | Linear OOA(3291, large, F32, 2, 7) | [i] | ||
| 30 | Linear OOA(3293, large, F32, 2, 7) | [i] | ||
| 31 | Linear OOA(3295, large, F32, 2, 7) | [i] | ||
| 32 | Linear OOA(3297, large, F32, 2, 7) | [i] | ||
| 33 | Linear OOA(3299, large, F32, 2, 7) | [i] | ||
| 34 | Linear OOA(32101, large, F32, 2, 7) | [i] | ||
| 35 | Linear OOA(32103, large, F32, 2, 7) | [i] | ||
| 36 | Linear OOA(32105, large, F32, 2, 7) | [i] | ||
| 37 | Linear OOA(32107, large, F32, 2, 7) | [i] | ||
| 38 | Linear OOA(32109, large, F32, 2, 7) | [i] | ||
| 39 | Linear OOA(3242, large, F32, 2, 7) | [i] | OOA Duplication | |
| 40 | Linear OOA(3241, 4194301, F32, 10, 7) (dual of [(4194301, 10), 41942969, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |