Information on Result #1131185
Linear OOA(2158, 699055, F2, 6, 15) (dual of [(699055, 6), 4194172, 16]-NRT-code), using OOA 6-folding based on linear OA(2158, 4194330, F2, 15) (dual of [4194330, 4194172, 16]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2155, 4194304, F2, 15) (dual of [4194304, 4194149, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 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 X4 applied to Ce(14) ⊂ Ce(12) [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(2159, 699055, F2, 6, 15) (dual of [(699055, 6), 4194171, 16]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2160, 699055, F2, 6, 15) (dual of [(699055, 6), 4194170, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(2157, 699054, F2, 6, 14) (dual of [(699054, 6), 4194167, 15]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2158, 699055, F2, 7, 15) (dual of [(699055, 7), 4893227, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2158, 699055, F2, 8, 15) (dual of [(699055, 8), 5592282, 16]-NRT-code) | [i] | ||
| 6 | Digital (143, 158, 699055)-net over F2 | [i] | ||