Information on Result #1097012
Linear OOA(2176, 416, F2, 5, 31) (dual of [(416, 5), 1904, 32]-NRT-code), using OOA 5-folding based on linear OA(2176, 2080, F2, 31) (dual of [2080, 1904, 32]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-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(30) ⊂ Ce(26) [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(2176, 416, F2, 5, 30) (dual of [(416, 5), 1904, 31]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2175, 415, F2, 5, 30) (dual of [(415, 5), 1900, 31]-NRT-code) | [i] | Truncation for OOAs | |