Information on Result #672805
Linear OA(2199, 4127, F2, 33) (dual of [4127, 3928, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,14]) based on
- linear OA(2193, 4097, F2, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2169, 4097, F2, 29) (dual of [4097, 3928, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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(2199, 4127, F2, 32) (dual of [4127, 3928, 33]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2200, 4128, F2, 33) (dual of [4128, 3928, 34]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2201, 4129, F2, 33) (dual of [4129, 3928, 34]-code) | [i] | ||
| 4 | Linear OA(2202, 4130, F2, 33) (dual of [4130, 3928, 34]-code) | [i] | ||
| 5 | Linear OA(2203, 4131, F2, 33) (dual of [4131, 3928, 34]-code) | [i] | ||
| 6 | Linear OA(2204, 4132, F2, 33) (dual of [4132, 3928, 34]-code) | [i] | ||
| 7 | Linear OA(2198, 4126, F2, 32) (dual of [4126, 3928, 33]-code) | [i] | Truncation | |
| 8 | Linear OOA(2199, 2063, F2, 2, 33) (dual of [(2063, 2), 3927, 34]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(2199, 1375, F2, 3, 33) (dual of [(1375, 3), 3926, 34]-NRT-code) | [i] | ||
| 10 | Linear OOA(2199, 1031, F2, 4, 33) (dual of [(1031, 4), 3925, 34]-NRT-code) | [i] | ||
| 11 | Linear OOA(2199, 825, F2, 5, 33) (dual of [(825, 5), 3926, 34]-NRT-code) | [i] | ||
| 12 | Linear OOA(2199, 687, F2, 6, 33) (dual of [(687, 6), 3923, 34]-NRT-code) | [i] | ||
| 13 | Linear OOA(2199, 589, F2, 7, 33) (dual of [(589, 7), 3924, 34]-NRT-code) | [i] | ||
| 14 | Linear OOA(2199, 515, F2, 8, 33) (dual of [(515, 8), 3921, 34]-NRT-code) | [i] | ||