Information on Result #1629806
Linear OOA(257, 774, F2, 5, 10) (dual of [(774, 5), 3813, 11]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(257, 774, F2, 2, 10) (dual of [(774, 2), 1491, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(257, 1030, F2, 2, 10) (dual of [(1030, 2), 2003, 11]-NRT-code), using
- strength reduction [i] based on linear OOA(257, 1030, F2, 2, 11) (dual of [(1030, 2), 2003, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(257, 2060, F2, 11) (dual of [2060, 2003, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(245, 2048, F2, 9) (dual of [2048, 2003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(10) ⊂ Ce(8) [i] based on
- OOA 2-folding [i] based on linear OA(257, 2060, F2, 11) (dual of [2060, 2003, 12]-code), using
- strength reduction [i] based on linear OOA(257, 1030, F2, 2, 11) (dual of [(1030, 2), 2003, 12]-NRT-code), using
Mode: 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(257, 773, F2, 6, 10) (dual of [(773, 6), 4581, 11]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(257, 773, F2, 7, 10) (dual of [(773, 7), 5354, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(257, 773, F2, 8, 10) (dual of [(773, 8), 6127, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(257, 773, F2, 15, 10) (dual of [(773, 15), 11538, 11]-NRT-code) | [i] | ||