Information on Result #2479986
Linear OOA(2214, 2064, F2, 2, 34) (dual of [(2064, 2), 3914, 35]-NRT-code), using 21 times duplication based on linear OOA(2213, 2064, F2, 2, 34) (dual of [(2064, 2), 3915, 35]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2211, 2063, F2, 2, 34) (dual of [(2063, 2), 3915, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2211, 4126, F2, 34) (dual of [4126, 3915, 35]-code), using
- strength reduction [i] based on linear OA(2211, 4126, F2, 35) (dual of [4126, 3915, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 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(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- strength reduction [i] based on linear OA(2211, 4126, F2, 35) (dual of [4126, 3915, 36]-code), using
- OOA 2-folding [i] based on linear OA(2211, 4126, F2, 34) (dual of [4126, 3915, 35]-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(2214, 1377, F2, 3, 34) (dual of [(1377, 3), 3917, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2214, 1377, F2, 4, 34) (dual of [(1377, 4), 5294, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2214, 1377, F2, 5, 34) (dual of [(1377, 5), 6671, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2214, 1377, F2, 6, 34) (dual of [(1377, 6), 8048, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(2214, 1377, F2, 7, 34) (dual of [(1377, 7), 9425, 35]-NRT-code) | [i] | ||
| 6 | Linear OOA(2214, 1377, F2, 8, 34) (dual of [(1377, 8), 10802, 35]-NRT-code) | [i] | ||
| 7 | Digital (180, 214, 1377)-net over F2 | [i] | ||