Information on Result #678145
Linear OA(4232, 1048597, F4, 31) (dual of [1048597, 1048365, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(4231, 1048576, F4, 31) (dual of [1048576, 1048345, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(41, 21, F4, 1) (dual of [21, 20, 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(4233, 1048598, F4, 31) (dual of [1048598, 1048365, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4234, 1048599, F4, 31) (dual of [1048599, 1048365, 32]-code) | [i] | ||
| 3 | Linear OA(4235, 1048600, F4, 31) (dual of [1048600, 1048365, 32]-code) | [i] | ||
| 4 | Linear OOA(4232, 524298, F4, 2, 31) (dual of [(524298, 2), 1048364, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4232, 349532, F4, 3, 31) (dual of [(349532, 3), 1048364, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(4232, 69906, F4, 31, 31) (dual of [(69906, 31), 2166854, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |