Information on Result #1630769
Linear OOA(297, 155717, F2, 5, 10) (dual of [(155717, 5), 778488, 11]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(297, 155717, F2, 3, 10) (dual of [(155717, 3), 467054, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(297, 174769, F2, 3, 10) (dual of [(174769, 3), 524210, 11]-NRT-code), using
- strength reduction [i] based on linear OOA(297, 174769, F2, 3, 11) (dual of [(174769, 3), 524210, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(297, 524307, F2, 11) (dual of [524307, 524210, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(297, 524308, F2, 11) (dual of [524308, 524211, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(296, 524288, F2, 11) (dual of [524288, 524192, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(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(10) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(297, 524308, F2, 11) (dual of [524308, 524211, 12]-code), using
- OOA 3-folding [i] based on linear OA(297, 524307, F2, 11) (dual of [524307, 524210, 12]-code), using
- strength reduction [i] based on linear OOA(297, 174769, F2, 3, 11) (dual of [(174769, 3), 524210, 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(297, 155716, F2, 6, 10) (dual of [(155716, 6), 934199, 11]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(297, 155716, F2, 7, 10) (dual of [(155716, 7), 1089915, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(297, 155716, F2, 8, 10) (dual of [(155716, 8), 1245631, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(297, 155716, F2, 15, 10) (dual of [(155716, 15), 2335643, 11]-NRT-code) | [i] | ||