Information on Result #2922682
Linear OOA(2246, 10926, F2, 6, 31) (dual of [(10926, 6), 65310, 32]-NRT-code), using 21 times duplication based on linear OOA(2245, 10926, F2, 6, 31) (dual of [(10926, 6), 65311, 32]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2245, 65556, F2, 31) (dual of [65556, 65311, 32]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2242, 65553, F2, 31) (dual of [65553, 65311, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2241, 65536, F2, 31) (dual of [65536, 65295, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2225, 65536, F2, 29) (dual of [65536, 65311, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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(30) ⊂ Ce(28) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(2242, 65553, F2, 31) (dual of [65553, 65311, 32]-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(2246, 10003, F2, 7, 31) (dual of [(10003, 7), 69775, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2246, 10003, F2, 8, 31) (dual of [(10003, 8), 79778, 32]-NRT-code) | [i] | ||
| 3 | Digital (215, 246, 10003)-net over F2 | [i] | ||