Information on Result #1651987
Linear OOA(3243, 128240, F3, 5, 31) (dual of [(128240, 5), 640957, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3243, 128240, F3, 4, 31) (dual of [(128240, 4), 512717, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 132863, F3, 4, 31) (dual of [(132863, 4), 531209, 32]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3242, 132863, F3, 4, 31) (dual of [(132863, 4), 531210, 32]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3242, 531452, F3, 31) (dual of [531452, 531210, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3242, 531454, F3, 31) (dual of [531454, 531212, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] 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
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3242, 531454, F3, 31) (dual of [531454, 531212, 32]-code), using
- OOA 4-folding [i] based on linear OA(3242, 531452, F3, 31) (dual of [531452, 531210, 32]-code), using
- 31 times duplication [i] based on linear OOA(3242, 132863, F3, 4, 31) (dual of [(132863, 4), 531210, 32]-NRT-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 OOA(3243, 42746, F3, 35, 31) (dual of [(42746, 35), 1495867, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |