Information on Result #672220
Linear OA(2254, 2097174, F2, 25) (dual of [2097174, 2096920, 26]-code), using construction X applied to Ce(24) ⊂ Ce(22) based on
- linear OA(2253, 2097152, F2, 25) (dual of [2097152, 2096899, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(2254, 2097174, F2, 24) (dual of [2097174, 2096920, 25]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2255, 2097175, F2, 25) (dual of [2097175, 2096920, 26]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2256, 2097176, F2, 25) (dual of [2097176, 2096920, 26]-code) | [i] | ||
| 4 | Linear OA(2257, 2097177, F2, 25) (dual of [2097177, 2096920, 26]-code) | [i] | ||
| 5 | Linear OA(2258, 2097178, F2, 25) (dual of [2097178, 2096920, 26]-code) | [i] | ||
| 6 | Linear OA(2253, 2097173, F2, 24) (dual of [2097173, 2096920, 25]-code) | [i] | Truncation | |
| 7 | Linear OOA(2254, 1048587, F2, 2, 25) (dual of [(1048587, 2), 2096920, 26]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2254, 699058, F2, 3, 25) (dual of [(699058, 3), 2096920, 26]-NRT-code) | [i] | ||
| 9 | Linear OOA(2254, 524293, F2, 4, 25) (dual of [(524293, 4), 2096918, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(2254, 419434, F2, 5, 25) (dual of [(419434, 5), 2096916, 26]-NRT-code) | [i] | ||
| 11 | Linear OOA(2254, 349529, F2, 6, 25) (dual of [(349529, 6), 2096920, 26]-NRT-code) | [i] | ||
| 12 | Linear OOA(2254, 299596, F2, 7, 25) (dual of [(299596, 7), 2096918, 26]-NRT-code) | [i] | ||
| 13 | Linear OOA(2254, 262146, F2, 8, 25) (dual of [(262146, 8), 2096914, 26]-NRT-code) | [i] | ||
| 14 | Linear OOA(2254, 174764, F2, 25, 25) (dual of [(174764, 25), 4368846, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |