Information on Result #672276
Linear OA(2222, 1048597, F2, 23) (dual of [1048597, 1048375, 24]-code), using construction X applied to Ce(22) ⊂ Ce(20) based on
- linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2201, 1048576, F2, 21) (dual of [1048576, 1048375, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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(2222, 1048597, F2, 22) (dual of [1048597, 1048375, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2223, 1048598, F2, 23) (dual of [1048598, 1048375, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2224, 1048599, F2, 23) (dual of [1048599, 1048375, 24]-code) | [i] | ||
| 4 | Linear OA(2225, 1048600, F2, 23) (dual of [1048600, 1048375, 24]-code) | [i] | ||
| 5 | Linear OA(2226, 1048601, F2, 23) (dual of [1048601, 1048375, 24]-code) | [i] | ||
| 6 | Linear OA(2221, 1048596, F2, 22) (dual of [1048596, 1048375, 23]-code) | [i] | Truncation | |
| 7 | Linear OOA(2222, 524298, F2, 2, 23) (dual of [(524298, 2), 1048374, 24]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2222, 349532, F2, 3, 23) (dual of [(349532, 3), 1048374, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2222, 262149, F2, 4, 23) (dual of [(262149, 4), 1048374, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2222, 209719, F2, 5, 23) (dual of [(209719, 5), 1048373, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2222, 174766, F2, 6, 23) (dual of [(174766, 6), 1048374, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2222, 149799, F2, 7, 23) (dual of [(149799, 7), 1048371, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2222, 131074, F2, 8, 23) (dual of [(131074, 8), 1048370, 24]-NRT-code) | [i] | ||
| 14 | Linear OOA(2222, 95326, F2, 23, 23) (dual of [(95326, 23), 2192276, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |