Information on Result #1511417
Linear OOA(2131, 850, F2, 3, 22) (dual of [(850, 3), 2419, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2131, 850, F2, 2, 22) (dual of [(850, 2), 1569, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2131, 1039, F2, 2, 22) (dual of [(1039, 2), 1947, 23]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2130, 1039, F2, 2, 22) (dual of [(1039, 2), 1948, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2128, 1038, F2, 2, 22) (dual of [(1038, 2), 1948, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2128, 2076, F2, 22) (dual of [2076, 1948, 23]-code), using
- strength reduction [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- strength reduction [i] based on linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using
- OOA 2-folding [i] based on linear OA(2128, 2076, F2, 22) (dual of [2076, 1948, 23]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2128, 1038, F2, 2, 22) (dual of [(1038, 2), 1948, 23]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2130, 1039, F2, 2, 22) (dual of [(1039, 2), 1948, 23]-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(2131, 425, F2, 5, 22) (dual of [(425, 5), 1994, 23]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2131, 425, F2, 6, 22) (dual of [(425, 6), 2419, 23]-NRT-code) | [i] | ||