Information on Result #1323520
Linear OA(4226, 1048651, F4, 29) (dual of [1048651, 1048425, 30]-code), using construction X applied to Ce(28) ⊂ Ce(20) based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(415, 75, F4, 7) (dual of [75, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
Mode: 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(4226, 1048651, F4, 28) (dual of [1048651, 1048425, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4227, 1048652, F4, 29) (dual of [1048652, 1048425, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4228, 1048653, F4, 29) (dual of [1048653, 1048425, 30]-code) | [i] | ||
| 4 | Linear OA(4225, 1048650, F4, 28) (dual of [1048650, 1048425, 29]-code) | [i] | Truncation | |
| 5 | Linear OA(4230, 1048656, F4, 29) (dual of [1048656, 1048426, 30]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(4231, 1048658, F4, 29) (dual of [1048658, 1048427, 30]-code) | [i] | ||
| 7 | Linear OOA(4226, 524325, F4, 2, 29) (dual of [(524325, 2), 1048424, 30]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4226, 349550, F4, 3, 29) (dual of [(349550, 3), 1048424, 30]-NRT-code) | [i] | ||