Information on Result #1649231
Linear OOA(3213, 51786, F3, 5, 29) (dual of [(51786, 5), 258717, 30]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3213, 51786, F3, 3, 29) (dual of [(51786, 3), 155145, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3213, 59053, F3, 3, 29) (dual of [(59053, 3), 176946, 30]-NRT-code), using
- 32 times duplication [i] based on linear OOA(3211, 59053, F3, 3, 29) (dual of [(59053, 3), 176948, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3211, 177159, F3, 29) (dual of [177159, 176948, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3210, 177158, F3, 29) (dual of [177158, 176948, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(3210, 177147, F3, 29) (dual of [177147, 176937, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3210, 177158, F3, 29) (dual of [177158, 176948, 30]-code), using
- OOA 3-folding [i] based on linear OA(3211, 177159, F3, 29) (dual of [177159, 176948, 30]-code), using
- 32 times duplication [i] based on linear OOA(3211, 59053, F3, 3, 29) (dual of [(59053, 3), 176948, 30]-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(3213, 17261, F3, 35, 29) (dual of [(17261, 35), 603922, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |