Information on Result #674517
Linear OA(3242, 531454, F3, 31) (dual of [531454, 531212, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(3241, 531441, F3, 31) (dual of [531441, 531200, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3229, 531441, F3, 29) (dual of [531441, 531212, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 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(3243, 531455, F3, 31) (dual of [531455, 531212, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3244, 531456, F3, 31) (dual of [531456, 531212, 32]-code) | [i] | ||
| 3 | Linear OA(3241, 531453, F3, 30) (dual of [531453, 531212, 31]-code) | [i] | Truncation | |
| 4 | Linear OOA(3242, 265727, F3, 2, 31) (dual of [(265727, 2), 531212, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3242, 177151, F3, 3, 31) (dual of [(177151, 3), 531211, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(3242, 132863, F3, 4, 31) (dual of [(132863, 4), 531210, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(3242, 106290, F3, 5, 31) (dual of [(106290, 5), 531208, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(3242, 35430, F3, 31, 31) (dual of [(35430, 31), 1098088, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |