Information on Result #805554
Linear OOA(279, 262155, F2, 2, 9) (dual of [(262155, 2), 524231, 10]-NRT-code), using OOA 2-folding based on linear OA(279, 524310, F2, 9) (dual of [524310, 524231, 10]-code), using
- 1 times code embedding in larger space [i] based on linear OA(278, 524309, F2, 9) (dual of [524309, 524231, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(277, 524288, F2, 9) (dual of [524288, 524211, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(258, 524288, F2, 7) (dual of [524288, 524230, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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
- construction X4 applied to Ce(8) ⊂ Ce(6) [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(279, 262155, F2, 2, 8) (dual of [(262155, 2), 524231, 9]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(280, 262155, F2, 2, 9) (dual of [(262155, 2), 524230, 10]-NRT-code) | [i] | OOA Duplication | |