Information on Result #1602784
Linear OOA(3103, 19687, F3, 4, 16) (dual of [(19687, 4), 78645, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3103, 19687, F3, 3, 16) (dual of [(19687, 3), 58958, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3103, 59061, F3, 16) (dual of [59061, 58958, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3102, 59060, F3, 16) (dual of [59060, 58958, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(391, 59049, F3, 14) (dual of [59049, 58958, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 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(15) ⊂ Ce(13) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3102, 59060, F3, 16) (dual of [59060, 58958, 17]-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(3104, 19687, F3, 4, 16) (dual of [(19687, 4), 78644, 17]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3103, 9843, F3, 20, 16) (dual of [(9843, 20), 196757, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |