Information on Result #735318
Linear OA(8178, 531774, F81, 21) (dual of [531774, 531696, 22]-code), using (u, u+v)-construction based on
- linear OA(8117, 330, F81, 10) (dual of [330, 313, 11]-code), using
- construction X applied to C([36,45]) ⊂ C([37,45]) [i] based on
- linear OA(8117, 328, F81, 10) (dual of [328, 311, 11]-code), using the BCH-code C(I) with length 328 | 812−1, defining interval I = {36,37,…,45}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(8115, 328, F81, 9) (dual of [328, 313, 10]-code), using the BCH-code C(I) with length 328 | 812−1, defining interval I = {37,38,…,45}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 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 C([36,45]) ⊂ C([37,45]) [i] based on
- linear OA(8161, 531444, F81, 21) (dual of [531444, 531383, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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 (see above)
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(8178, 265887, F81, 2, 21) (dual of [(265887, 2), 531696, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8178, 177258, F81, 3, 21) (dual of [(177258, 3), 531696, 22]-NRT-code) | [i] | ||