Information on Result #2697258
Linear OOA(761, large, F7, 3, 5), using 6 times NRT-code embedding in larger space based on linear OOA(743, large, F7, 3, 5), using
- (u, u+v)-construction [i] based on
- linear OOA(79, 6725601, F7, 3, 2) (dual of [(6725601, 3), 20176794, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(79, 6725601, F7, 2, 2) (dual of [(6725601, 2), 13451193, 3]-NRT-code), using
- appending kth column [i] based on linear OA(79, 6725601, F7, 2) (dual of [6725601, 6725592, 3]-code), using
- Hamming code H(9,7) [i]
- appending kth column [i] based on linear OA(79, 6725601, F7, 2) (dual of [6725601, 6725592, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(79, 6725601, F7, 2, 2) (dual of [(6725601, 2), 13451193, 3]-NRT-code), using
- linear OOA(734, 5764804, F7, 3, 5) (dual of [(5764804, 3), 17294378, 6]-NRT-code), using
- trace code [i] based on linear OOA(4917, 2882402, F49, 3, 5) (dual of [(2882402, 3), 8647189, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(4917, 5764805, F49, 5) (dual of [5764805, 5764788, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(4917, 5764805, F49, 5) (dual of [5764805, 5764788, 6]-code), using
- trace code [i] based on linear OOA(4917, 2882402, F49, 3, 5) (dual of [(2882402, 3), 8647189, 6]-NRT-code), using
- linear OOA(79, 6725601, F7, 3, 2) (dual of [(6725601, 3), 20176794, 3]-NRT-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(762, large, F7, 3, 5) | [i] | OOA Duplication | |