Information on Result #2480578
Linear OOA(2237, 1048, F2, 2, 41) (dual of [(1048, 2), 1859, 42]-NRT-code), using 21 times duplication based on linear OOA(2236, 1048, F2, 2, 41) (dual of [(1048, 2), 1860, 42]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2234, 1047, F2, 2, 41) (dual of [(1047, 2), 1860, 42]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2234, 2094, F2, 41) (dual of [2094, 1860, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(213, 46, F2, 5) (dual of [46, 33, 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(40) ⊂ Ce(34) [i] based on
- OOA 2-folding [i] based on linear OA(2234, 2094, F2, 41) (dual of [2094, 1860, 42]-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(2237, 1038, F2, 3, 41) (dual of [(1038, 3), 2877, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2237, 1038, F2, 4, 41) (dual of [(1038, 4), 3915, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(2237, 1038, F2, 5, 41) (dual of [(1038, 5), 4953, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(2237, 1038, F2, 6, 41) (dual of [(1038, 6), 5991, 42]-NRT-code) | [i] | ||
| 5 | Linear OOA(2237, 1038, F2, 7, 41) (dual of [(1038, 7), 7029, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(2237, 1038, F2, 8, 41) (dual of [(1038, 8), 8067, 42]-NRT-code) | [i] | ||
| 7 | Digital (196, 237, 1038)-net over F2 | [i] | ||