Information on Result #672205
Linear OA(2260, 2097202, F2, 25) (dual of [2097202, 2096942, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(2253, 2097153, F2, 25) (dual of [2097153, 2096900, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2211, 2097153, F2, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-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(2260, 2097202, F2, 24) (dual of [2097202, 2096942, 25]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2259, 2097201, F2, 24) (dual of [2097201, 2096942, 25]-code) | [i] | Truncation | |
| 3 | Linear OOA(2260, 1048601, F2, 2, 25) (dual of [(1048601, 2), 2096942, 26]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2260, 699067, F2, 3, 25) (dual of [(699067, 3), 2096941, 26]-NRT-code) | [i] | ||
| 5 | Linear OOA(2260, 524300, F2, 4, 25) (dual of [(524300, 4), 2096940, 26]-NRT-code) | [i] | ||
| 6 | Linear OOA(2260, 419440, F2, 5, 25) (dual of [(419440, 5), 2096940, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(2260, 349533, F2, 6, 25) (dual of [(349533, 6), 2096938, 26]-NRT-code) | [i] | ||
| 8 | Linear OOA(2260, 299600, F2, 7, 25) (dual of [(299600, 7), 2096940, 26]-NRT-code) | [i] | ||
| 9 | Linear OOA(2260, 262150, F2, 8, 25) (dual of [(262150, 8), 2096940, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(2260, 174766, F2, 25, 25) (dual of [(174766, 25), 4368890, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |