Information on Result #678109
Linear OA(4212, 1048587, F4, 29) (dual of [1048587, 1048375, 30]-code), using construction X applied to Ce(28) ⊂ Ce(26) 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(4201, 1048576, F4, 27) (dual of [1048576, 1048375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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(4213, 1048588, F4, 29) (dual of [1048588, 1048375, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4211, 1048586, F4, 28) (dual of [1048586, 1048375, 29]-code) | [i] | Truncation | |
| 3 | Linear OOA(4212, 524293, F4, 2, 29) (dual of [(524293, 2), 1048374, 30]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4212, 349529, F4, 3, 29) (dual of [(349529, 3), 1048375, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(4212, 74899, F4, 29, 29) (dual of [(74899, 29), 2171859, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |