Information on Result #1651589
Linear OOA(3239, 21823, F3, 5, 35) (dual of [(21823, 5), 108876, 36]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3239, 21823, F3, 2, 35) (dual of [(21823, 2), 43407, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3239, 29543, F3, 2, 35) (dual of [(29543, 2), 58847, 36]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3238, 29543, F3, 2, 35) (dual of [(29543, 2), 58848, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3238, 59086, F3, 35) (dual of [59086, 58848, 36]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3237, 59085, F3, 35) (dual of [59085, 58848, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(3231, 59049, F3, 35) (dual of [59049, 58818, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3237, 59085, F3, 35) (dual of [59085, 58848, 36]-code), using
- OOA 2-folding [i] based on linear OA(3238, 59086, F3, 35) (dual of [59086, 58848, 36]-code), using
- 31 times duplication [i] based on linear OOA(3238, 29543, F3, 2, 35) (dual of [(29543, 2), 58848, 36]-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(3239, 5455, F3, 45, 35) (dual of [(5455, 45), 245236, 36]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |