Information on Result #2611708
Linear OOA(2114, 1398110, F2, 3, 10) (dual of [(1398110, 3), 4194216, 11]-NRT-code), using strength reduction based on linear OOA(2114, 1398110, F2, 3, 11) (dual of [(1398110, 3), 4194216, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2114, 4194330, F2, 11) (dual of [4194330, 4194216, 12]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2112, 4194328, F2, 11) (dual of [4194328, 4194216, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(2111, 4194304, F2, 11) (dual of [4194304, 4194193, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(289, 4194304, F2, 9) (dual of [4194304, 4194215, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(10) ⊂ Ce(8) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2112, 4194328, F2, 11) (dual of [4194328, 4194216, 12]-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(2114, 1109874, F2, 4, 10) (dual of [(1109874, 4), 4439382, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2114, 1109874, F2, 5, 10) (dual of [(1109874, 5), 5549256, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(2114, 1109874, F2, 6, 10) (dual of [(1109874, 6), 6659130, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(2114, 1109874, F2, 7, 10) (dual of [(1109874, 7), 7769004, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(2114, 1109874, F2, 8, 10) (dual of [(1109874, 8), 8878878, 11]-NRT-code) | [i] | ||
| 6 | Digital (104, 114, 1109874)-net over F2 | [i] | ||