Information on Result #731607
Linear OA(1682, 131076, F16, 21) (dual of [131076, 130994, 22]-code), using trace code based on linear OA(25641, 65538, F256, 21) (dual of [65538, 65497, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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 OA(1683, 131077, F16, 21) (dual of [131077, 130994, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1695, 131114, F16, 21) (dual of [131114, 131019, 22]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(1682, 65538, F16, 2, 21) (dual of [(65538, 2), 130994, 22]-NRT-code) | [i] | OOA Folding | |