Information on Result #2521308
Linear OOA(8154, large, F81, 2, 4), using 19 times NRT-code embedding in larger space based on linear OOA(8116, large, F81, 2, 4), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(810, s, F81, 2, 0) for arbitrarily large s, using
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
- linear OOA(811, 265722, F81, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 2, 1) for arbitrarily large s, using
- linear OOA(811, 265722, F81, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code) (see above)
- linear OOA(814, 265722, F81, 2, 2) (dual of [(265722, 2), 531440, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 538084, F81, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
- appending kth column [i] based on linear OA(814, 538084, F81, 2) (dual of [538084, 538080, 3]-code), using
- Hamming code H(4,81) [i]
- appending kth column [i] based on linear OA(814, 538084, F81, 2) (dual of [538084, 538080, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 538084, F81, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
- linear OOA(8110, 265722, F81, 2, 4) (dual of [(265722, 2), 531434, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8110, 531444, F81, 4) (dual of [531444, 531434, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(817, 531441, F81, 3) (dual of [531441, 531434, 4]-code or 531441-cap in PG(6,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- OOA 2-folding [i] based on linear OA(8110, 531444, F81, 4) (dual of [531444, 531434, 5]-code), using
- linear OOA(810, 265722, F81, 2, 0) (dual of [(265722, 2), 531444, 1]-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(8155, large, F81, 2, 4) | [i] | OOA Duplication |