Information on Result #2866582
Linear OOA(2244, 6557, F2, 5, 32) (dual of [(6557, 5), 32541, 33]-NRT-code), using 21 times duplication based on linear OOA(2243, 6557, F2, 5, 32) (dual of [(6557, 5), 32542, 33]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2243, 32785, F2, 32) (dual of [32785, 32542, 33]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2241, 32783, F2, 32) (dual of [32783, 32542, 33]-code), using
- 1 times truncation [i] based on linear OA(2242, 32784, F2, 33) (dual of [32784, 32542, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2241, 32768, F2, 33) (dual of [32768, 32527, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(2242, 32784, F2, 33) (dual of [32784, 32542, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2241, 32783, F2, 32) (dual of [32783, 32542, 33]-code), 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 OOA(2244, 6134, F2, 6, 32) (dual of [(6134, 6), 36560, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2244, 6134, F2, 7, 32) (dual of [(6134, 7), 42694, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2244, 6134, F2, 8, 32) (dual of [(6134, 8), 48828, 33]-NRT-code) | [i] | ||
| 4 | Digital (212, 244, 6134)-net over F2 | [i] | ||