Information on Result #1054015
Linear OOA(2253, 4110, F2, 4, 34) (dual of [(4110, 4), 16187, 35]-NRT-code), using OOA 4-folding based on linear OA(2253, 16440, F2, 34) (dual of [16440, 16187, 35]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2251, 16438, F2, 34) (dual of [16438, 16187, 35]-code), using
- 1 times truncation [i] based on linear OA(2252, 16439, F2, 35) (dual of [16439, 16187, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2197, 16384, F2, 29) (dual of [16384, 16187, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(213, 55, F2, 5) (dual of [55, 42, 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(34) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(2252, 16439, F2, 35) (dual of [16439, 16187, 36]-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(2254, 4110, F2, 4, 34) (dual of [(4110, 4), 16186, 35]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2253, 4110, F2, 5, 34) (dual of [(4110, 5), 20297, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2253, 4110, F2, 6, 34) (dual of [(4110, 6), 24407, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2253, 4110, F2, 7, 34) (dual of [(4110, 7), 28517, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(2253, 4110, F2, 8, 34) (dual of [(4110, 8), 32627, 35]-NRT-code) | [i] | ||
| 6 | Digital (219, 253, 4110)-net over F2 | [i] | ||