Information on Result #2676881
Linear OOA(3113, 59053, F3, 3, 16) (dual of [(59053, 3), 177046, 17]-NRT-code), using 31 times duplication based on linear OOA(3112, 59053, F3, 3, 16) (dual of [(59053, 3), 177047, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3112, 177159, F3, 16) (dual of [177159, 177047, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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
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 OOA(3113, 59053, F3, 4, 16) (dual of [(59053, 4), 236099, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3113, 59053, F3, 5, 16) (dual of [(59053, 5), 295152, 17]-NRT-code) | [i] | ||
| 3 | Digital (97, 113, 59053)-net over F3 | [i] | ||