Information on Result #672264
Linear OA(2208, 1048624, F2, 21) (dual of [1048624, 1048416, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(2201, 1048577, F2, 21) (dual of [1048577, 1048376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2161, 1048577, F2, 17) (dual of [1048577, 1048416, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 47, F2, 3) (dual of [47, 40, 4]-code or 47-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2208, 1048624, F2, 20) (dual of [1048624, 1048416, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2209, 1048625, F2, 21) (dual of [1048625, 1048416, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2210, 1048626, F2, 21) (dual of [1048626, 1048416, 22]-code) | [i] | ||
| 4 | Linear OA(2207, 1048623, F2, 20) (dual of [1048623, 1048416, 21]-code) | [i] | Truncation | |
| 5 | Linear OOA(2208, 524312, F2, 2, 21) (dual of [(524312, 2), 1048416, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2208, 349541, F2, 3, 21) (dual of [(349541, 3), 1048415, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2208, 262156, F2, 4, 21) (dual of [(262156, 4), 1048416, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2208, 209724, F2, 5, 21) (dual of [(209724, 5), 1048412, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2208, 174770, F2, 6, 21) (dual of [(174770, 6), 1048412, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2208, 149803, F2, 7, 21) (dual of [(149803, 7), 1048413, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2208, 131078, F2, 8, 21) (dual of [(131078, 8), 1048416, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2208, 104862, F2, 21, 21) (dual of [(104862, 21), 2201894, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |