Information on Result #2219898
Linear OA(239, 524308, F2, 4) (dual of [524308, 524269, 5]-code), using 1 times truncation based on linear OA(240, 524309, F2, 5) (dual of [524309, 524269, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(239, 524288, F2, 5) (dual of [524288, 524249, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(220, 524288, F2, 3) (dual of [524288, 524268, 4]-code or 524288-cap in PG(19,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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
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(239, 524308, F2, 2, 4) (dual of [(524308, 2), 1048577, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(239, 524308, F2, 3, 4) (dual of [(524308, 3), 1572885, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(239, 262154, F2, 2, 4) (dual of [(262154, 2), 524269, 5]-NRT-code) | [i] | OOA Folding | |