Information on Result #673050
Linear OA(2257, 1035, F2, 53) (dual of [1035, 778, 54]-code), using construction X applied to Ce(52) ⊂ Ce(50) based on
- linear OA(2256, 1024, F2, 53) (dual of [1024, 768, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2246, 1024, F2, 51) (dual of [1024, 778, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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 OA(2256, 1034, F2, 52) (dual of [1034, 778, 53]-code) | [i] | Truncation | |
| 2 | Linear OOA(2257, 517, F2, 2, 53) (dual of [(517, 2), 777, 54]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2257, 345, F2, 3, 53) (dual of [(345, 3), 778, 54]-NRT-code) | [i] | ||
| 4 | Linear OOA(2257, 258, F2, 4, 53) (dual of [(258, 4), 775, 54]-NRT-code) | [i] | ||
| 5 | Linear OOA(2257, 207, F2, 5, 53) (dual of [(207, 5), 778, 54]-NRT-code) | [i] | ||
| 6 | Linear OOA(2257, 172, F2, 6, 53) (dual of [(172, 6), 775, 54]-NRT-code) | [i] | ||
| 7 | Linear OOA(2257, 147, F2, 7, 53) (dual of [(147, 7), 772, 54]-NRT-code) | [i] | ||