Information on Result #947976
Linear OOA(2260, 2747, F2, 3, 38) (dual of [(2747, 3), 7981, 39]-NRT-code), using OOA 3-folding based on linear OA(2260, 8241, F2, 38) (dual of [8241, 7981, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(2260, 8243, F2, 38) (dual of [8243, 7983, 39]-code), using
- construction X applied to Ce(38) ⊂ Ce(32) [i] based on
- linear OA(2248, 8192, F2, 39) (dual of [8192, 7944, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2209, 8192, F2, 33) (dual of [8192, 7983, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(212, 51, F2, 4) (dual of [51, 39, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 63, F2, 4) (dual of [63, 51, 5]-code), using
- the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(212, 63, F2, 4) (dual of [63, 51, 5]-code), using
- construction X applied to Ce(38) ⊂ Ce(32) [i] based on
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(2260, 2503, F2, 4, 38) (dual of [(2503, 4), 9752, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2260, 2503, F2, 5, 38) (dual of [(2503, 5), 12255, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(2260, 2503, F2, 6, 38) (dual of [(2503, 6), 14758, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(2260, 2503, F2, 7, 38) (dual of [(2503, 7), 17261, 39]-NRT-code) | [i] | ||
| 5 | Linear OOA(2260, 2503, F2, 8, 38) (dual of [(2503, 8), 19764, 39]-NRT-code) | [i] | ||
| 6 | Digital (222, 260, 2503)-net over F2 | [i] | ||