Information on Result #1166335
Linear OOA(2249, 65538, F2, 8, 27) (dual of [(65538, 8), 524055, 28]-NRT-code), using OOA 8-folding based on linear OA(2249, 524304, F2, 27) (dual of [524304, 524055, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2249, 524308, F2, 27) (dual of [524308, 524059, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2229, 524288, F2, 25) (dual of [524288, 524059, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [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(2249, 65538, F2, 8, 26) (dual of [(65538, 8), 524055, 27]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2250, 65538, F2, 8, 27) (dual of [(65538, 8), 524054, 28]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2251, 65538, F2, 8, 27) (dual of [(65538, 8), 524053, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(2252, 65538, F2, 8, 27) (dual of [(65538, 8), 524052, 28]-NRT-code) | [i] | ||
| 5 | Digital (222, 249, 65538)-net over F2 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |