Information on Result #2668942
Linear OOA(2249, 2748, F2, 3, 37) (dual of [(2748, 3), 7995, 38]-NRT-code), using 21 times duplication based on linear OOA(2248, 2748, F2, 3, 37) (dual of [(2748, 3), 7996, 38]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2248, 8244, F2, 37) (dual of [8244, 7996, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- linear OA(2235, 8192, F2, 37) (dual of [8192, 7957, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(213, 52, F2, 5) (dual of [52, 39, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [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(2249, 2261, F2, 4, 37) (dual of [(2261, 4), 8795, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2249, 2261, F2, 5, 37) (dual of [(2261, 5), 11056, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(2249, 2261, F2, 6, 37) (dual of [(2261, 6), 13317, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2249, 2261, F2, 7, 37) (dual of [(2261, 7), 15578, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(2249, 2261, F2, 8, 37) (dual of [(2261, 8), 17839, 38]-NRT-code) | [i] | ||
| 6 | Digital (212, 249, 2261)-net over F2 | [i] | ||