Information on Result #1513073
Linear OOA(2165, 898, F2, 3, 28) (dual of [(898, 3), 2529, 29]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2165, 898, F2, 2, 28) (dual of [(898, 2), 1631, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2165, 1042, F2, 2, 28) (dual of [(1042, 2), 1919, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2165, 2084, F2, 28) (dual of [2084, 1919, 29]-code), using
- 1 times truncation [i] based on linear OA(2166, 2085, F2, 29) (dual of [2085, 1919, 30]-code), using
- construction XX applied to Ce(28) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2155, 2048, F2, 29) (dual of [2048, 1893, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2133, 2048, F2, 25) (dual of [2048, 1915, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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 XX applied to Ce(28) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2166, 2085, F2, 29) (dual of [2085, 1919, 30]-code), using
- OOA 2-folding [i] based on linear OA(2165, 2084, F2, 28) (dual of [2084, 1919, 29]-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(2165, 449, F2, 5, 28) (dual of [(449, 5), 2080, 29]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2165, 449, F2, 6, 28) (dual of [(449, 6), 2529, 29]-NRT-code) | [i] | ||