Information on Result #672817
Linear OA(2127, 4127, F2, 21) (dual of [4127, 4000, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(2121, 4097, F2, 21) (dual of [4097, 3976, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(297, 4097, F2, 17) (dual of [4097, 4000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [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
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 OA(2127, 4127, F2, 20) (dual of [4127, 4000, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2128, 4128, F2, 21) (dual of [4128, 4000, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2129, 4129, F2, 21) (dual of [4129, 4000, 22]-code) | [i] | ||
| 4 | Linear OA(2130, 4130, F2, 21) (dual of [4130, 4000, 22]-code) | [i] | ||
| 5 | Linear OA(2126, 4126, F2, 20) (dual of [4126, 4000, 21]-code) | [i] | Truncation | |
| 6 | Linear OOA(2127, 2063, F2, 2, 21) (dual of [(2063, 2), 3999, 22]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2127, 1375, F2, 3, 21) (dual of [(1375, 3), 3998, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2127, 1031, F2, 4, 21) (dual of [(1031, 4), 3997, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2127, 825, F2, 5, 21) (dual of [(825, 5), 3998, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2127, 687, F2, 6, 21) (dual of [(687, 6), 3995, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2127, 589, F2, 7, 21) (dual of [(589, 7), 3996, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2127, 515, F2, 8, 21) (dual of [(515, 8), 3993, 22]-NRT-code) | [i] | ||
| 13 | Linear OOA(2127, 412, F2, 21, 21) (dual of [(412, 21), 8525, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |