Information on Result #672259
Linear OA(2248, 1048624, F2, 25) (dual of [1048624, 1048376, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(2241, 1048577, F2, 25) (dual of [1048577, 1048336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(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(2248, 1048624, F2, 24) (dual of [1048624, 1048376, 25]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2249, 1048625, F2, 25) (dual of [1048625, 1048376, 26]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2250, 1048626, F2, 25) (dual of [1048626, 1048376, 26]-code) | [i] | ||
| 4 | Linear OA(2251, 1048627, F2, 25) (dual of [1048627, 1048376, 26]-code) | [i] | ||
| 5 | Linear OA(2252, 1048628, F2, 25) (dual of [1048628, 1048376, 26]-code) | [i] | ||
| 6 | Linear OA(2247, 1048623, F2, 24) (dual of [1048623, 1048376, 25]-code) | [i] | Truncation | |
| 7 | Linear OOA(2248, 524312, F2, 2, 25) (dual of [(524312, 2), 1048376, 26]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2248, 349541, F2, 3, 25) (dual of [(349541, 3), 1048375, 26]-NRT-code) | [i] | ||
| 9 | Linear OOA(2248, 262156, F2, 4, 25) (dual of [(262156, 4), 1048376, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(2248, 209724, F2, 5, 25) (dual of [(209724, 5), 1048372, 26]-NRT-code) | [i] | ||
| 11 | Linear OOA(2248, 174770, F2, 6, 25) (dual of [(174770, 6), 1048372, 26]-NRT-code) | [i] | ||
| 12 | Linear OOA(2248, 149803, F2, 7, 25) (dual of [(149803, 7), 1048373, 26]-NRT-code) | [i] | ||
| 13 | Linear OOA(2248, 131078, F2, 8, 25) (dual of [(131078, 8), 1048376, 26]-NRT-code) | [i] | ||
| 14 | Linear OOA(2248, 87385, F2, 25, 25) (dual of [(87385, 25), 2184377, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |