Information on Result #2668821
Linear OOA(2221, 1370, F2, 3, 36) (dual of [(1370, 3), 3889, 37]-NRT-code), using 22 times duplication based on linear OOA(2219, 1370, F2, 3, 36) (dual of [(1370, 3), 3891, 37]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2219, 4110, F2, 36) (dual of [4110, 3891, 37]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2217, 4108, F2, 36) (dual of [4108, 3891, 37]-code), using
- 1 times truncation [i] based on linear OA(2218, 4109, F2, 37) (dual of [4109, 3891, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(2217, 4096, F2, 37) (dual of [4096, 3879, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(36) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(2218, 4109, F2, 37) (dual of [4109, 3891, 38]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2217, 4108, F2, 36) (dual of [4108, 3891, 37]-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(2221, 1370, F2, 4, 36) (dual of [(1370, 4), 5259, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2221, 1370, F2, 5, 36) (dual of [(1370, 5), 6629, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(2221, 1370, F2, 6, 36) (dual of [(1370, 6), 7999, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(2221, 1370, F2, 7, 36) (dual of [(1370, 7), 9369, 37]-NRT-code) | [i] | ||
| 5 | Linear OOA(2221, 1370, F2, 8, 36) (dual of [(1370, 8), 10739, 37]-NRT-code) | [i] | ||
| 6 | Digital (185, 221, 1370)-net over F2 | [i] | ||